Abstract group data - 9000.o

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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': 60, 'aut_gen_orders': [20, 4, 12, 20, 12], 'aut_gens': [[1, 12, 120, 360, 1800], [197, 5316, 8160, 3240, 1800], [7273, 8364, 5880, 1440, 7200], [3365, 7428, 8760, 5400, 6120], [3553, 8316, 6000, 360, 7560], [5545, 7428, 4440, 5400, 6120]], 'aut_group': None, 'aut_hash': 9056236928001170395, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24000, 'aut_permdeg': 142, 'aut_perms': [6305272414242887059426578678321553369260281456352809910310134029639890750484460027579361036705636040274264226769503914134012639170362023088058552550153282420007526082598100551174841379621234022025091624219390900159714403067362450158698833842950, 159702007891857697698146808975708009605794611996087052873616980783079576628870865442821548532431404437196244857528852921544626036027593649764379423122910623302261583500753774385365151652373894253807022889031811193621693037027971708193900344148174, 268447636188760560829050854936783894908457827881992175053391314630480119338608984928299369839373927708754644901503570169360288319714613164488956170170915763442161204740394494010250181445913498858670401680260293864305928017236388783835378735508802, 204956542203982195499446150503782617163252684625366533042748246673644349231698829744605712256026123965743992971336823335374576464728144061846690419183948987231699293695662903386405761978019798316048061504762752916629849297429423242291964871931623, 138478588004196894520796397144826298903298267101126154278018141372278284908305935306462654001441200892367883558788432298964245705385082790614618638385544279211208946583185609685131257620654905146288038860835244404748801284361801401157341300198761], 'aut_phi_ratio': 10.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 15, 1, 1], [2, 75, 1, 1], [2, 125, 1, 1], [3, 1, 2, 1], [3, 50, 1, 1], [3, 50, 2, 1], [4, 125, 1, 2], [4, 375, 1, 2], [5, 4, 1, 1], [5, 12, 1, 2], [5, 12, 4, 1], [5, 24, 2, 1], [6, 15, 2, 1], [6, 75, 2, 1], [6, 125, 2, 1], [6, 250, 1, 1], [6, 250, 2, 1], [10, 60, 1, 2], [10, 60, 4, 1], [10, 300, 1, 1], [12, 125, 2, 2], [12, 250, 1, 2], [12, 250, 2, 2], [12, 375, 2, 2], [15, 4, 2, 1], [15, 12, 2, 2], [15, 12, 8, 1], [15, 24, 4, 1], [15, 200, 1, 1], [15, 200, 2, 1], [30, 60, 2, 2], [30, 60, 8, 1], [30, 300, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_5^3.(C_4^2\\times S_3)', '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': 60, 'autcentquo_group': '12000.cm', 'autcentquo_hash': 5340715652065179242, 'autcentquo_nilpotent': False, 'autcentquo_order': 12000, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_5^3:(S_3\\times C_4^2)', 'cc_stats': [[1, 1, 1], [2, 15, 1], [2, 75, 1], [2, 125, 1], [3, 1, 2], [3, 50, 3], [4, 125, 2], [4, 375, 2], [5, 4, 1], [5, 12, 6], [5, 24, 2], [6, 15, 2], [6, 75, 2], [6, 125, 2], [6, 250, 3], [10, 60, 6], [10, 300, 1], [12, 125, 4], [12, 250, 6], [12, 375, 4], [15, 4, 2], [15, 12, 12], [15, 24, 4], [15, 200, 3], [30, 60, 12], [30, 300, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '3000.bf', 'commutator_count': 1, 'commutator_label': '375.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '5.1', '5.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 15, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['3000.bf', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 15, 1, 1], [2, 75, 1, 1], [2, 125, 1, 1], [3, 1, 2, 1], [3, 50, 1, 1], [3, 50, 2, 1], [4, 125, 2, 1], [4, 375, 2, 1], [5, 4, 1, 1], [5, 12, 1, 6], [5, 24, 1, 2], [6, 15, 2, 1], [6, 75, 2, 1], [6, 125, 2, 1], [6, 250, 1, 1], [6, 250, 2, 1], [10, 60, 1, 6], [10, 300, 1, 1], [12, 125, 4, 1], [12, 250, 2, 1], [12, 250, 4, 1], [12, 375, 4, 1], [15, 4, 2, 1], [15, 12, 2, 6], [15, 24, 2, 2], [15, 200, 1, 1], [15, 200, 2, 1], [30, 60, 2, 6], [30, 300, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 576, 'exponent': 60, 'exponents_of_order': [3, 3, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[12, 0, 16], [24, 0, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '9000.o', 'hash': 1735341798720924668, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [4, 10, 3, 5, 5], 'inner_gens': [[1, 1236, 3840, 3600, 720], [5737, 12, 6360, 360, 7560], [4921, 972, 120, 3240, 1440], [5761, 12, 8040, 360, 1800], [2881, 5052, 2280, 360, 1800]], 'inner_hash': 3629711919683738508, 'inner_nilpotent': False, 'inner_order': 3000, 'inner_split': True, 'inner_tex': 'C_5^3:(C_4\\times S_3)', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 24], [2, 12], [4, 6], [8, 3], [12, 36], [24, 6]], 'label': '9000.o', 'linC_count': 16, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 32, 'linQ_dim': 14, 'linQ_dim_count': 32, 'linR_count': 64, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C5^3:(S3*C12)', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 44, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 87, 'number_divisions': 52, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 248, 'number_subgroup_classes': 356, 'number_subgroups': 14168, 'old_label': None, 'order': 9000, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 215], [3, 152], [4, 1000], [5, 124], [6, 1180], [10, 660], [12, 3500], [15, 848], [30, 1320]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [1208, 24], 'outer_gens': [[1205, 1212, 4800, 1800, 3240], [49, 12, 840, 720, 3600]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 10], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 7], [8, 4], [12, 12], [16, 1], [24, 14], [48, 2]], 'representations': {'PC': {'code': '100150550806413291036784627529661301996636702880962974953856348810262400591398111', 'gens': [1, 4, 6, 7, 8], 'pres': [8, -2, -2, -3, -2, -5, -3, -5, 5, 16, 41, 39555, 1739, 91, 2884, 1932, 184325, 11533, 25469, 201606, 40334, 1558, 46087, 230415, 40351, 815]}, 'Perm': {'d': 18, 'gens': [401818317466347, 779836733359444]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5^3:(S_3\\times C_{12})', 'transitive_degree': 45, '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: 111104274
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 15, 'group_order': 9000, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 111104285
    {'aut_label': '2A', 'centralizer': '15.a1.a1', 'counter': 2, 'group_counter': 15, 'group_order': 9000, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 60, 'size': 15}
  • id: 111104296
    {'aut_label': '2B', 'centralizer': '75.e1.a1', 'counter': 3, 'group_counter': 15, 'group_order': 9000, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 426, 'size': 75}
  • id: 111104307
    {'aut_label': '2C', 'centralizer': '125.a1.a1', 'counter': 4, 'group_counter': 15, 'group_order': 9000, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 54, 'size': 125}
  • id: 111104318
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 15, 'group_order': 9000, 'label': '3A1', 'order': 3, 'powers': [6, 1, 6], 'representative': 8, 'size': 1}
  • id: 111104329
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 15, 'group_order': 9000, 'label': '3A-1', 'order': 3, 'powers': [5, 1, 5], 'representative': 4, 'size': 1}
  • id: 111104340
    {'aut_label': '3B', 'centralizer': '50.b1.a1', 'counter': 7, 'group_counter': 15, 'group_order': 9000, 'label': '3B', 'order': 3, 'powers': [7, 1, 7], 'representative': 6360, 'size': 50}
  • id: 111104351
    {'aut_label': '3C1', 'centralizer': '50.b1.a1', 'counter': 8, 'group_counter': 15, 'group_order': 9000, 'label': '3C1', 'order': 3, 'powers': [9, 1, 9], 'representative': 964, 'size': 50}
  • id: 111104360
    {'aut_label': '3C1', 'centralizer': '50.b1.a1', 'counter': 9, 'group_counter': 15, 'group_order': 9000, 'label': '3C-1', 'order': 3, 'powers': [8, 1, 8], 'representative': 6248, 'size': 50}
  • id: 111104275
    {'aut_label': '4A1', 'centralizer': '125.a1.a1', 'counter': 10, 'group_counter': 15, 'group_order': 9000, 'label': '4A1', 'order': 4, 'powers': [4, 11, 10], 'representative': 6735, 'size': 125}
  • id: 111104276
    {'aut_label': '4A-1', 'centralizer': '125.a1.a1', 'counter': 11, 'group_counter': 15, 'group_order': 9000, 'label': '4A-1', 'order': 4, 'powers': [4, 10, 11], 'representative': 6093, 'size': 125}
  • id: 111104277
    {'aut_label': '4B1', 'centralizer': '375.a1.a1', 'counter': 12, 'group_counter': 15, 'group_order': 9000, 'label': '4B1', 'order': 4, 'powers': [4, 13, 12], 'representative': 99, 'size': 375}
  • id: 111104278
    {'aut_label': '4B-1', 'centralizer': '375.a1.a1', 'counter': 13, 'group_counter': 15, 'group_order': 9000, 'label': '4B-1', 'order': 4, 'powers': [4, 12, 13], 'representative': 81, 'size': 375}
  • id: 111104279
    {'aut_label': '5A', 'centralizer': '4.a1.a1', 'counter': 14, 'group_counter': 15, 'group_order': 9000, 'label': '5A', 'order': 5, 'powers': [14, 14, 1], 'representative': 72, 'size': 4}
  • id: 111104280
    {'aut_label': '5B', 'centralizer': '12.e1.a1', 'counter': 15, 'group_counter': 15, 'group_order': 9000, 'label': '5B', 'order': 5, 'powers': [15, 15, 1], 'representative': 1152, 'size': 12}
  • id: 111104281
    {'aut_label': '5B', 'centralizer': '12.e1.a1', 'counter': 16, 'group_counter': 15, 'group_order': 9000, 'label': '5C', 'order': 5, 'powers': [16, 16, 1], 'representative': 432, 'size': 12}
  • id: 111104282
    {'aut_label': '5B', 'centralizer': '12.e1.a1', 'counter': 17, 'group_counter': 15, 'group_order': 9000, 'label': '5D', 'order': 5, 'powers': [17, 17, 1], 'representative': 1872, 'size': 12}
  • id: 111104283
    {'aut_label': '5B', 'centralizer': '12.e1.a1', 'counter': 18, 'group_counter': 15, 'group_order': 9000, 'label': '5E', 'order': 5, 'powers': [18, 18, 1], 'representative': 792, 'size': 12}
  • id: 111104284
    {'aut_label': '5F', 'centralizer': '12.e1.a1', 'counter': 19, 'group_counter': 15, 'group_order': 9000, 'label': '5F', 'order': 5, 'powers': [19, 19, 1], 'representative': 1080, 'size': 12}
  • id: 111104286
    {'aut_label': '5G', 'centralizer': '12.f1.a1', 'counter': 20, 'group_counter': 15, 'group_order': 9000, 'label': '5G', 'order': 5, 'powers': [20, 20, 1], 'representative': 5760, 'size': 12}
  • id: 111104287
    {'aut_label': '5H', 'centralizer': '24.a1.a1', 'counter': 21, 'group_counter': 15, 'group_order': 9000, 'label': '5H', 'order': 5, 'powers': [21, 21, 1], 'representative': 6552, 'size': 24}
  • id: 111104288
    {'aut_label': '5H', 'centralizer': '24.a1.a1', 'counter': 22, 'group_counter': 15, 'group_order': 9000, 'label': '5I', 'order': 5, 'powers': [22, 22, 1], 'representative': 2952, 'size': 24}
  • id: 111104289
    {'aut_label': '6A1', 'centralizer': '15.a1.a1', 'counter': 23, 'group_counter': 15, 'group_order': 9000, 'label': '6A1', 'order': 6, 'powers': [6, 2, 24], 'representative': 68, 'size': 15}
  • id: 111104290
    {'aut_label': '6A1', 'centralizer': '15.a1.a1', 'counter': 24, 'group_counter': 15, 'group_order': 9000, 'label': '6A-1', 'order': 6, 'powers': [5, 2, 23], 'representative': 64, 'size': 15}
  • id: 111104291
    {'aut_label': '6B1', 'centralizer': '75.e1.a1', 'counter': 25, 'group_counter': 15, 'group_order': 9000, 'label': '6B1', 'order': 6, 'powers': [5, 3, 26], 'representative': 430, 'size': 75}
  • id: 111104292
    {'aut_label': '6B1', 'centralizer': '75.e1.a1', 'counter': 26, 'group_counter': 15, 'group_order': 9000, 'label': '6B-1', 'order': 6, 'powers': [6, 3, 25], 'representative': 422, 'size': 75}
  • id: 111104293
    {'aut_label': '6C1', 'centralizer': '125.a1.a1', 'counter': 27, 'group_counter': 15, 'group_order': 9000, 'label': '6C1', 'order': 6, 'powers': [6, 4, 28], 'representative': 50, 'size': 125}
  • id: 111104294
    {'aut_label': '6C1', 'centralizer': '125.a1.a1', 'counter': 28, 'group_counter': 15, 'group_order': 9000, 'label': '6C-1', 'order': 6, 'powers': [5, 4, 27], 'representative': 58, 'size': 125}
  • id: 111104295
    {'aut_label': '6D', 'centralizer': '250.b1.a1', 'counter': 29, 'group_counter': 15, 'group_order': 9000, 'label': '6D', 'order': 6, 'powers': [7, 4, 29], 'representative': 8046, 'size': 250}
  • id: 111104297
    {'aut_label': '6E1', 'centralizer': '250.b1.a1', 'counter': 30, 'group_counter': 15, 'group_order': 9000, 'label': '6E1', 'order': 6, 'powers': [8, 4, 31], 'representative': 4898, 'size': 250}
  • id: 111104298
    {'aut_label': '6E1', 'centralizer': '250.b1.a1', 'counter': 31, 'group_counter': 15, 'group_order': 9000, 'label': '6E-1', 'order': 6, 'powers': [9, 4, 30], 'representative': 2866, 'size': 250}
  • id: 111104299
    {'aut_label': '10A', 'centralizer': '60.b1.a1', 'counter': 32, 'group_counter': 15, 'group_order': 9000, 'label': '10A', 'order': 10, 'powers': [14, 32, 2], 'representative': 36, 'size': 60}
  • id: 111104300
    {'aut_label': '10B', 'centralizer': '60.b1.a1', 'counter': 33, 'group_counter': 15, 'group_order': 9000, 'label': '10B', 'order': 10, 'powers': [15, 33, 2], 'representative': 2196, 'size': 60}
  • id: 111104301
    {'aut_label': '10B', 'centralizer': '60.b1.a1', 'counter': 34, 'group_counter': 15, 'group_order': 9000, 'label': '10C', 'order': 10, 'powers': [16, 34, 2], 'representative': 1116, 'size': 60}
  • id: 111104302
    {'aut_label': '10B', 'centralizer': '60.b1.a1', 'counter': 35, 'group_counter': 15, 'group_order': 9000, 'label': '10D', 'order': 10, 'powers': [17, 35, 2], 'representative': 3756, 'size': 60}
  • id: 111104303
    {'aut_label': '10B', 'centralizer': '60.b1.a1', 'counter': 36, 'group_counter': 15, 'group_order': 9000, 'label': '10E', 'order': 10, 'powers': [18, 36, 2], 'representative': 396, 'size': 60}
  • id: 111104304
    {'aut_label': '10F', 'centralizer': '60.b1.a1', 'counter': 37, 'group_counter': 15, 'group_order': 9000, 'label': '10F', 'order': 10, 'powers': [19, 37, 2], 'representative': 2220, 'size': 60}
  • id: 111104305
    {'aut_label': '10G', 'centralizer': '300.f1.a1', 'counter': 38, 'group_counter': 15, 'group_order': 9000, 'label': '10G', 'order': 10, 'powers': [20, 38, 3], 'representative': 8706, 'size': 300}
  • id: 111104306
    {'aut_label': '12A1', 'centralizer': '125.a1.a1', 'counter': 39, 'group_counter': 15, 'group_order': 9000, 'label': '12A1', 'order': 12, 'powers': [28, 10, 41], 'representative': 353, 'size': 125}
  • id: 111104308
    {'aut_label': '12A-1', 'centralizer': '125.a1.a1', 'counter': 40, 'group_counter': 15, 'group_order': 9000, 'label': '12A-1', 'order': 12, 'powers': [27, 11, 42], 'representative': 7531, 'size': 125}
  • id: 111104309
    {'aut_label': '12A1', 'centralizer': '125.a1.a1', 'counter': 41, 'group_counter': 15, 'group_order': 9000, 'label': '12A5', 'order': 12, 'powers': [27, 10, 39], 'representative': 349, 'size': 125}
  • id: 111104310
    {'aut_label': '12A-1', 'centralizer': '125.a1.a1', 'counter': 42, 'group_counter': 15, 'group_order': 9000, 'label': '12A-5', 'order': 12, 'powers': [28, 11, 40], 'representative': 7535, 'size': 125}
  • id: 111104311
    {'aut_label': '12B1', 'centralizer': '250.b1.a1', 'counter': 43, 'group_counter': 15, 'group_order': 9000, 'label': '12B1', 'order': 12, 'powers': [29, 11, 43], 'representative': 8823, 'size': 250}
  • id: 111104312
    {'aut_label': '12B-1', 'centralizer': '250.b1.a1', 'counter': 44, 'group_counter': 15, 'group_order': 9000, 'label': '12B-1', 'order': 12, 'powers': [29, 10, 44], 'representative': 3669, 'size': 250}
  • id: 111104313
    {'aut_label': '12C1', 'centralizer': '250.b1.a1', 'counter': 45, 'group_counter': 15, 'group_order': 9000, 'label': '12C1', 'order': 12, 'powers': [30, 10, 47], 'representative': 2005, 'size': 250}
  • id: 111104314
    {'aut_label': '12C-1', 'centralizer': '250.b1.a1', 'counter': 46, 'group_counter': 15, 'group_order': 9000, 'label': '12C-1', 'order': 12, 'powers': [31, 11, 48], 'representative': 2183, 'size': 250}
  • id: 111104315
    {'aut_label': '12C1', 'centralizer': '250.b1.a1', 'counter': 47, 'group_counter': 15, 'group_order': 9000, 'label': '12C5', 'order': 12, 'powers': [31, 10, 45], 'representative': 8369, 'size': 250}
  • id: 111104316
    {'aut_label': '12C-1', 'centralizer': '250.b1.a1', 'counter': 48, 'group_counter': 15, 'group_order': 9000, 'label': '12C-5', 'order': 12, 'powers': [30, 11, 46], 'representative': 7339, 'size': 250}
  • id: 111104317
    {'aut_label': '12D1', 'centralizer': '375.a1.a1', 'counter': 49, 'group_counter': 15, 'group_order': 9000, 'label': '12D1', 'order': 12, 'powers': [27, 12, 51], 'representative': 73, 'size': 375}
  • id: 111104319
    {'aut_label': '12D-1', 'centralizer': '375.a1.a1', 'counter': 50, 'group_counter': 15, 'group_order': 9000, 'label': '12D-1', 'order': 12, 'powers': [28, 13, 52], 'representative': 107, 'size': 375}
  • id: 111104320
    {'aut_label': '12D1', 'centralizer': '375.a1.a1', 'counter': 51, 'group_counter': 15, 'group_order': 9000, 'label': '12D5', 'order': 12, 'powers': [28, 12, 49], 'representative': 77, 'size': 375}
  • id: 111104321
    {'aut_label': '12D-1', 'centralizer': '375.a1.a1', 'counter': 52, 'group_counter': 15, 'group_order': 9000, 'label': '12D-5', 'order': 12, 'powers': [27, 13, 50], 'representative': 103, 'size': 375}
  • id: 111104322
    {'aut_label': '15A1', 'centralizer': '4.a1.a1', 'counter': 53, 'group_counter': 15, 'group_order': 9000, 'label': '15A1', 'order': 15, 'powers': [54, 14, 6], 'representative': 32, 'size': 4}
  • id: 111104323
    {'aut_label': '15A1', 'centralizer': '4.a1.a1', 'counter': 54, 'group_counter': 15, 'group_order': 9000, 'label': '15A-1', 'order': 15, 'powers': [53, 14, 5], 'representative': 100, 'size': 4}
  • id: 111104324
    {'aut_label': '15B1', 'centralizer': '12.e1.a1', 'counter': 55, 'group_counter': 15, 'group_order': 9000, 'label': '15B1', 'order': 15, 'powers': [56, 15, 6], 'representative': 392, 'size': 12}
  • id: 111104325
    {'aut_label': '15B1', 'centralizer': '12.e1.a1', 'counter': 56, 'group_counter': 15, 'group_order': 9000, 'label': '15B-1', 'order': 15, 'powers': [55, 15, 5], 'representative': 1540, 'size': 12}
  • id: 111104326
    {'aut_label': '15B1', 'centralizer': '12.e1.a1', 'counter': 57, 'group_counter': 15, 'group_order': 9000, 'label': '15C1', 'order': 15, 'powers': [58, 16, 6], 'representative': 752, 'size': 12}
  • id: 111104327
    {'aut_label': '15B1', 'centralizer': '12.e1.a1', 'counter': 58, 'group_counter': 15, 'group_order': 9000, 'label': '15C-1', 'order': 15, 'powers': [57, 16, 5], 'representative': 1180, 'size': 12}
  • id: 111104328
    {'aut_label': '15B1', 'centralizer': '12.e1.a1', 'counter': 59, 'group_counter': 15, 'group_order': 9000, 'label': '15D1', 'order': 15, 'powers': [60, 17, 6], 'representative': 3632, 'size': 12}
  • id: 111104330
    {'aut_label': '15B1', 'centralizer': '12.e1.a1', 'counter': 60, 'group_counter': 15, 'group_order': 9000, 'label': '15D-1', 'order': 15, 'powers': [59, 17, 5], 'representative': 5500, 'size': 12}
  • id: 111104331
    {'aut_label': '15B1', 'centralizer': '12.e1.a1', 'counter': 61, 'group_counter': 15, 'group_order': 9000, 'label': '15E1', 'order': 15, 'powers': [62, 18, 6], 'representative': 1472, 'size': 12}
  • id: 111104332
    {'aut_label': '15B1', 'centralizer': '12.e1.a1', 'counter': 62, 'group_counter': 15, 'group_order': 9000, 'label': '15E-1', 'order': 15, 'powers': [61, 18, 5], 'representative': 460, 'size': 12}
  • id: 111104333
    {'aut_label': '15F1', 'centralizer': '12.e1.a1', 'counter': 63, 'group_counter': 15, 'group_order': 9000, 'label': '15F1', 'order': 15, 'powers': [64, 19, 6], 'representative': 368, 'size': 12}
  • id: 111104334
    {'aut_label': '15F1', 'centralizer': '12.e1.a1', 'counter': 64, 'group_counter': 15, 'group_order': 9000, 'label': '15F-1', 'order': 15, 'powers': [63, 19, 5], 'representative': 1444, 'size': 12}
  • id: 111104335
    {'aut_label': '15G1', 'centralizer': '12.f1.a1', 'counter': 65, 'group_counter': 15, 'group_order': 9000, 'label': '15G1', 'order': 15, 'powers': [66, 20, 5], 'representative': 2524, 'size': 12}
  • id: 111104336
    {'aut_label': '15G1', 'centralizer': '12.f1.a1', 'counter': 66, 'group_counter': 15, 'group_order': 9000, 'label': '15G-1', 'order': 15, 'powers': [65, 20, 6], 'representative': 8288, 'size': 12}
  • id: 111104337
    {'aut_label': '15H1', 'centralizer': '24.a1.a1', 'counter': 67, 'group_counter': 15, 'group_order': 9000, 'label': '15H1', 'order': 15, 'powers': [68, 21, 5], 'representative': 2188, 'size': 24}
  • id: 111104338
    {'aut_label': '15H1', 'centralizer': '24.a1.a1', 'counter': 68, 'group_counter': 15, 'group_order': 9000, 'label': '15H-1', 'order': 15, 'powers': [67, 21, 6], 'representative': 2192, 'size': 24}
  • id: 111104339
    {'aut_label': '15H1', 'centralizer': '24.a1.a1', 'counter': 69, 'group_counter': 15, 'group_order': 9000, 'label': '15I1', 'order': 15, 'powers': [70, 22, 5], 'representative': 3988, 'size': 24}
  • id: 111104341
    {'aut_label': '15H1', 'centralizer': '24.a1.a1', 'counter': 70, 'group_counter': 15, 'group_order': 9000, 'label': '15I-1', 'order': 15, 'powers': [69, 22, 6], 'representative': 3992, 'size': 24}
  • id: 111104342
    {'aut_label': '15J', 'centralizer': '200.a1.a1', 'counter': 71, 'group_counter': 15, 'group_order': 9000, 'label': '15J', 'order': 15, 'powers': [71, 14, 7], 'representative': 3456, 'size': 200}
  • id: 111104343
    {'aut_label': '15K1', 'centralizer': '200.a1.a1', 'counter': 72, 'group_counter': 15, 'group_order': 9000, 'label': '15K1', 'order': 15, 'powers': [73, 14, 9], 'representative': 316, 'size': 200}
  • id: 111104344
    {'aut_label': '15K1', 'centralizer': '200.a1.a1', 'counter': 73, 'group_counter': 15, 'group_order': 9000, 'label': '15K-1', 'order': 15, 'powers': [72, 14, 8], 'representative': 176, 'size': 200}
  • id: 111104345
    {'aut_label': '30A1', 'centralizer': '60.b1.a1', 'counter': 74, 'group_counter': 15, 'group_order': 9000, 'label': '30A1', 'order': 30, 'powers': [53, 32, 23], 'representative': 16, 'size': 60}
  • id: 111104346
    {'aut_label': '30A1', 'centralizer': '60.b1.a1', 'counter': 75, 'group_counter': 15, 'group_order': 9000, 'label': '30A-1', 'order': 30, 'powers': [54, 32, 24], 'representative': 20, 'size': 60}
  • id: 111104347
    {'aut_label': '30B1', 'centralizer': '60.b1.a1', 'counter': 76, 'group_counter': 15, 'group_order': 9000, 'label': '30B1', 'order': 30, 'powers': [55, 33, 23], 'representative': 1816, 'size': 60}
  • id: 111104348
    {'aut_label': '30B1', 'centralizer': '60.b1.a1', 'counter': 77, 'group_counter': 15, 'group_order': 9000, 'label': '30B-1', 'order': 30, 'powers': [56, 33, 24], 'representative': 1820, 'size': 60}
  • id: 111104349
    {'aut_label': '30B1', 'centralizer': '60.b1.a1', 'counter': 78, 'group_counter': 15, 'group_order': 9000, 'label': '30C1', 'order': 30, 'powers': [57, 34, 23], 'representative': 376, 'size': 60}
  • id: 111104350
    {'aut_label': '30B1', 'centralizer': '60.b1.a1', 'counter': 79, 'group_counter': 15, 'group_order': 9000, 'label': '30C-1', 'order': 30, 'powers': [58, 34, 24], 'representative': 380, 'size': 60}
  • id: 111104352
    {'aut_label': '30B1', 'centralizer': '60.b1.a1', 'counter': 80, 'group_counter': 15, 'group_order': 9000, 'label': '30D1', 'order': 30, 'powers': [59, 35, 23], 'representative': 136, 'size': 60}
  • id: 111104353
    {'aut_label': '30B1', 'centralizer': '60.b1.a1', 'counter': 81, 'group_counter': 15, 'group_order': 9000, 'label': '30D-1', 'order': 30, 'powers': [60, 35, 24], 'representative': 140, 'size': 60}
  • id: 111104354
    {'aut_label': '30B1', 'centralizer': '60.b1.a1', 'counter': 82, 'group_counter': 15, 'group_order': 9000, 'label': '30E1', 'order': 30, 'powers': [61, 36, 23], 'representative': 736, 'size': 60}
  • id: 111104355
    {'aut_label': '30B1', 'centralizer': '60.b1.a1', 'counter': 83, 'group_counter': 15, 'group_order': 9000, 'label': '30E-1', 'order': 30, 'powers': [62, 36, 24], 'representative': 740, 'size': 60}
  • id: 111104356
    {'aut_label': '30F1', 'centralizer': '60.b1.a1', 'counter': 84, 'group_counter': 15, 'group_order': 9000, 'label': '30F1', 'order': 30, 'powers': [63, 37, 23], 'representative': 1864, 'size': 60}
  • id: 111104357
    {'aut_label': '30F1', 'centralizer': '60.b1.a1', 'counter': 85, 'group_counter': 15, 'group_order': 9000, 'label': '30F-1', 'order': 30, 'powers': [64, 37, 24], 'representative': 1868, 'size': 60}
  • id: 111104358
    {'aut_label': '30G1', 'centralizer': '300.f1.a1', 'counter': 86, 'group_counter': 15, 'group_order': 9000, 'label': '30G1', 'order': 30, 'powers': [65, 38, 25], 'representative': 6182, 'size': 300}
  • id: 111104359
    {'aut_label': '30G1', 'centralizer': '300.f1.a1', 'counter': 87, 'group_counter': 15, 'group_order': 9000, 'label': '30G-1', 'order': 30, 'powers': [66, 38, 26], 'representative': 3670, 'size': 300}
• 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: 4854129
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4854140
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4854151
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4854162
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4854173
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4854177
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 4854178
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1g', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 4854179
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -1, -1, 2, -1, -1, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -1, -1, 2, -1, -1, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4854180
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -1, -1, 2, -1, -1, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -1, -1, 2, -1, -1, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4854130
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, -1, -1, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4854133
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854134
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 0, 2, 2, 2, -1, -1, -1, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854131
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1k', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, -2, -2, 4, -2, -2, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, -2, -2, 2, 2, -4, 2, 2, -4, -4, -4, -4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 4, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2], 'schur_index': 1}
  • id: 4854132
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.1l', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -2, -2, 4, -2, -2, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, 2, 2, 2, 2, -4, 2, 2, 4, 4, 4, 4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2], 'schur_index': 1}
  • id: 4854135
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.2c', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 0, 0, 4, -2, -2, -2, 1, 1, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 1, -2, 1, 1, 1, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854136
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.2d', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 0, 0, -4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -4, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854137
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.2e', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 0, 0, 4, -2, -2, -2, 1, 1, -4, -4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854139
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.4a', 'multiplicity': 1, 'nt': [5, 3], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, -1, 4, -1, -1, -1, 4, -1, -1, -1, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 4, 4, 4, -1, -1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, -1, -1, 4, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4854141
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.4b', 'multiplicity': 1, 'nt': [10, 5], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, -1, 4, -1, -1, -1, 4, -1, -1, -1, -4, -4, 0, 0, 0, 0, 0, 0, 0, -4, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 4, 4, 4, -1, -1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -4, 1, 1, -4, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4854138
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.2f', 'multiplicity': 4, 'nt': [24, 65], 'qdim': 8, 'qvalues': [8, 0, 0, -8, -4, -4, -4, 2, 2, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 4, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854142
    {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.4c', 'multiplicity': 2, 'nt': [15, 8], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -4, -4, 8, -4, -4, 0, 0, 0, 0, -2, 8, -2, -2, -2, 8, -2, -2, -2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 8, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, -4, -4, -4, 1, 1, -4, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, 1, 1, -4, 1, 1, -4, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4854143
    {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.4d', 'multiplicity': 2, 'nt': [30, 26], 'qdim': 8, 'qvalues': [8, -8, 0, 0, -4, -4, 8, -4, -4, 0, 0, 0, 0, -2, 8, -2, -2, -2, 8, -2, -2, -2, 4, 4, 0, 0, 0, 0, 0, 0, 0, -8, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, -4, -4, -4, 1, 1, -4, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, -1, -1, -1, -1, -1, 4, -1, -1, 4, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4854144
    {'cdim': 8, 'counter': 23, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.8a', 'multiplicity': 1, 'nt': [15, 11], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, -4, -4, -4, 0, 0, 0, 0, -2, 8, -2, -2, -2, 8, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 8, 8, 8, -2, -2, 8, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854146
    {'cdim': 12, 'counter': 25, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12a', 'multiplicity': 1, 'nt': [15, 27], 'qdim': 12, 'qvalues': [12, 0, 4, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, 12, -3, 2, 2, 2, 2, 2, -3, -3, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 2, 2, 2, 2, -3, -3, 2, 2, 2, 2, 2, 2, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4854147
    {'cdim': 12, 'counter': 26, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12b', 'multiplicity': 1, 'nt': [15, 27], 'qdim': 12, 'qvalues': [12, 4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, 12, 2, -3, -3, -3, -3, -3, 2, 2, 4, 4, 0, 0, 0, 0, 0, 0, 0, -1, -1, 4, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, -3, -3, -3, -3, 2, 2, -3, -3, -3, -3, -3, -3, 2, 2, 2, 2, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 4, -1, -1, -1, 4, 0, 0], 'schur_index': 1}
  • id: 4854148
    {'cdim': 12, 'counter': 27, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12c', 'multiplicity': 1, 'nt': [15, 49], 'qdim': 12, 'qvalues': [12, 4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, -3, 2, -3, 2, 7, -3, -3, 2, -3, 4, 4, 0, 0, 0, 0, 0, 0, 0, -1, 4, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 2, -3, 7, -3, 2, 2, -3, 2, -3, 7, -3, -3, 2, 2, -3, -3, 0, 0, 0, -1, -1, 4, -1, -1, -1, 4, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4854149
    {'cdim': 12, 'counter': 28, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12d', 'multiplicity': 1, 'nt': [15, 49], 'qdim': 12, 'qvalues': [12, 4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, -3, 2, -3, 7, -3, -3, 2, -3, 2, 4, 4, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 7, 2, -3, -3, 2, 2, -3, 7, -3, -3, -3, 2, -3, -3, 2, 2, 0, 0, 0, -1, -1, -1, 4, 4, -1, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4854150
    {'cdim': 12, 'counter': 29, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12e', 'multiplicity': 1, 'nt': [15, 49], 'qdim': 12, 'qvalues': [12, 4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, -3, 2, 2, -3, -3, -3, 7, 2, -3, 4, 4, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, 7, -3, -3, 2, 2, 2, -3, -3, -3, 2, 7, 2, 2, -3, -3, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, -1, 0, 0], 'schur_index': 1}
  • id: 4854152
    {'cdim': 12, 'counter': 30, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12f', 'multiplicity': 1, 'nt': [15, 49], 'qdim': 12, 'qvalues': [12, 4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, -3, 2, 7, -3, 2, -3, -3, -3, 2, 4, 4, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 2, -3, 2, 2, 7, -3, -3, 2, 7, -3, -3, -3, 2, 2, 0, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4854153
    {'cdim': 12, 'counter': 31, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12g', 'multiplicity': 1, 'nt': [30, 150], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, 12, 2, -3, -3, -3, -3, -3, 2, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 1, 1, -4, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, -3, -3, -3, -3, 2, 2, -3, -3, -3, -3, -3, -3, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, -4, 1, 1, 1, -4, 0, 0], 'schur_index': 1}
  • id: 4854154
    {'cdim': 12, 'counter': 32, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12h', 'multiplicity': 1, 'nt': [30, 150], 'qdim': 12, 'qvalues': [12, 0, -4, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, 12, -3, 2, 2, 2, 2, 2, -3, -3, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, 2, 2, 2, 2, -3, -3, 2, 2, 2, 2, 2, 2, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4854155
    {'cdim': 12, 'counter': 33, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12i', 'multiplicity': 1, 'nt': [30, 433], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, -3, 2, -3, 2, 7, -3, -3, 2, -3, -4, -4, 0, 0, 0, 0, 0, 0, 0, 1, -4, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 2, -3, 7, -3, 2, 2, -3, 2, -3, 7, -3, -3, 2, 2, -3, -3, 0, 0, 0, 1, 1, -4, 1, 1, 1, -4, 1, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4854156
    {'cdim': 12, 'counter': 34, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12j', 'multiplicity': 1, 'nt': [30, 433], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, -3, 2, -3, 7, -3, -3, 2, -3, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 7, 2, -3, -3, 2, 2, -3, 7, -3, -3, -3, 2, -3, -3, 2, 2, 0, 0, 0, 1, 1, 1, -4, -4, 1, 1, 1, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4854157
    {'cdim': 12, 'counter': 35, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12k', 'multiplicity': 1, 'nt': [30, 433], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, -3, 2, 2, -3, -3, -3, 7, 2, -3, -4, -4, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -4, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, 7, -3, -3, 2, 2, 2, -3, -3, -3, 2, 7, 2, 2, -3, -3, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, 1, 0, 0], 'schur_index': 1}
  • id: 4854158
    {'cdim': 12, 'counter': 36, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12l', 'multiplicity': 1, 'nt': [30, 433], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 12, 12, 0, 0, 0, 0, 0, 0, 0, -3, 2, 7, -3, 2, -3, -3, -3, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, 2, -3, 2, 2, 7, -3, -3, 2, 7, -3, -3, -3, 2, 2, 0, 0, 0, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4854145
    {'cdim': 8, 'counter': 24, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.8b', 'multiplicity': 2, 'nt': [30, 91], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -8, -8, -8, 4, 4, 0, 0, 0, 0, -4, 16, -4, -4, -4, 16, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -8, -8, -8, 2, 2, -8, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854159
    {'cdim': 12, 'counter': 37, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12m', 'multiplicity': 2, 'nt': [45, 215], 'qdim': 24, 'qvalues': [24, 0, 8, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, 24, -6, 4, 4, 4, 4, 4, -6, -6, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, -2, -2, -2, -2, 3, 3, -2, -2, -2, -2, -2, -2, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 4854160
    {'cdim': 12, 'counter': 38, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12n', 'multiplicity': 2, 'nt': [45, 215], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, 24, 4, -6, -6, -6, -6, -6, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, 8, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 3, 3, 3, 3, -2, -2, 3, 3, 3, 3, 3, 3, -2, -2, -2, -2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, -4, 1, 1, 1, -4, 0, 0], 'schur_index': 1}
  • id: 4854161
    {'cdim': 12, 'counter': 39, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12o', 'multiplicity': 2, 'nt': [45, 473], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 4, -6, 4, 14, -6, -6, 4, -6, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, 8, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -2, 3, -7, 3, -2, -2, 3, -2, 3, -7, 3, 3, -2, -2, 3, 3, 0, 0, 0, 1, 1, -4, 1, 1, 1, -4, 1, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4854163
    {'cdim': 12, 'counter': 40, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12p', 'multiplicity': 2, 'nt': [45, 473], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 4, -6, 14, -6, -6, 4, -6, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 8, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -7, -2, 3, 3, -2, -2, 3, -7, 3, 3, 3, -2, 3, 3, -2, -2, 0, 0, 0, 1, 1, 1, -4, -4, 1, 1, 1, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4854164
    {'cdim': 12, 'counter': 41, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12q', 'multiplicity': 2, 'nt': [45, 473], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 4, 4, -6, -6, -6, 14, 4, -6, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 8, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, -7, 3, 3, -2, -2, -2, 3, 3, 3, -2, -7, -2, -2, 3, 3, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, 1, 0, 0], 'schur_index': 1}
  • id: 4854165
    {'cdim': 12, 'counter': 42, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12r', 'multiplicity': 2, 'nt': [45, 473], 'qdim': 24, 'qvalues': [24, 8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 4, 14, -6, 4, -6, -6, -6, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -2, 3, -2, -2, -7, 3, 3, -2, -7, 3, 3, 3, -2, -2, 0, 0, 0, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 4854166
    {'cdim': 12, 'counter': 43, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12s', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 4, -6, 4, 14, -6, -6, 4, -6, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, -8, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -2, 3, -7, 3, -2, -2, 3, -2, 3, -7, 3, 3, -2, -2, 3, 3, 0, 0, 0, -1, -1, 4, -1, -1, -1, 4, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4854167
    {'cdim': 12, 'counter': 44, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12t', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 4, -6, 14, -6, -6, 4, -6, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -7, -2, 3, 3, -2, -2, 3, -7, 3, 3, 3, -2, 3, 3, -2, -2, 0, 0, 0, -1, -1, -1, 4, 4, -1, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4854168
    {'cdim': 12, 'counter': 45, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12u', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 4, 4, -6, -6, -6, 14, 4, -6, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -8, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, -7, 3, 3, -2, -2, -2, 3, 3, 3, -2, -7, -2, -2, 3, 3, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, -1, 0, 0], 'schur_index': 1}
  • id: 4854169
    {'cdim': 12, 'counter': 46, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12v', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, -6, 4, 14, -6, 4, -6, -6, -6, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 3, 3, -2, 3, -2, -2, -7, 3, 3, -2, -7, 3, 3, 3, -2, -2, 0, 0, 0, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 4854170
    {'cdim': 12, 'counter': 47, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12w', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, 24, 4, -6, -6, -6, -6, -6, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, -8, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 3, 3, 3, 3, -2, -2, 3, 3, 3, 3, 3, 3, -2, -2, -2, -2, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 4, -1, -1, -1, 4, 0, 0], 'schur_index': 1}
  • id: 4854171
    {'cdim': 12, 'counter': 48, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.12x', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 24, 'qvalues': [24, 0, -8, 0, -12, -12, 0, 0, 0, 0, 0, 0, 0, 24, -6, 4, 4, 4, 4, 4, -6, -6, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, -2, -2, -2, -2, 3, 3, -2, -2, -2, -2, -2, -2, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 4854172
    {'cdim': 24, 'counter': 49, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.24a', 'multiplicity': 1, 'nt': [30, 435], 'qdim': 24, 'qvalues': [24, 0, 0, 0, 24, 24, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, 4, 4, 4, -1, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 4, 4, 4, -6, -6, -6, -6, 4, 4, -6, 4, -1, -1, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854174
    {'cdim': 24, 'counter': 50, 'faithful': False, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.24b', 'multiplicity': 1, 'nt': [30, 435], 'qdim': 24, 'qvalues': [24, 0, 0, 0, 24, 24, 0, 0, 0, 0, 0, 0, 0, -6, -6, 4, 4, -6, 4, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 4, -6, -6, 4, -6, -6, 4, 4, 4, -6, 4, -6, 4, 4, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854175
    {'cdim': 24, 'counter': 51, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.24c', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, -24, -24, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, -12, 8, 8, 8, -2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, -4, -4, -4, 6, 6, 6, 6, -4, -4, 6, -4, 1, 1, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4854176
    {'cdim': 24, 'counter': 52, 'faithful': True, 'group': '9000.o', 'group_order': 9000, 'image': None, 'label': '9000.o.24d', 'multiplicity': 2, 'nt': [90, 0], 'qdim': 48, 'qvalues': [48, 0, 0, 0, -24, -24, 0, 0, 0, 0, 0, 0, 0, -12, -12, 8, 8, -12, 8, -12, 8, -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, 6, 6, -4, 6, 6, -4, 6, 6, -4, -4, -4, 6, -4, 6, -4, -4, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
• gps_char •

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

  
  
  • id: 8002630
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 9000, 'label': '9000.o.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 8002641
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 4500, 'label': '9000.o.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 8002652
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 4500, 'label': '9000.o.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 8002663
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 4500, 'label': '9000.o.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 8002674
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 3000, 'label': '9000.o.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[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]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 8002685
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 3000, 'label': '9000.o.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[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]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 8002696
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 2250, 'label': '9000.o.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 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, 0]], [[-1, 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, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 8002707
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 2250, 'label': '9000.o.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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, 0]], [[-1, 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, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 8002716
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 2250, 'label': '9000.o.1g1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 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, 0]], [[-1, 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, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 8002631
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 2250, 'label': '9000.o.1g2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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, 0]], [[-1, 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, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 8002632
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 1500, 'label': '9000.o.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[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, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-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]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 8002633
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 1500, 'label': '9000.o.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[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, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-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]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 8002634
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 1500, 'label': '9000.o.1i1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[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, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[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]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 8002635
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 1500, 'label': '9000.o.1i2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[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, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[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]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 8002636
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 1500, 'label': '9000.o.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-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]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 8002637
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 1500, 'label': '9000.o.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-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]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 8002638
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 17, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 750, 'label': '9000.o.1k1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 3]], [[-1, 5]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[1, 4]]]}
  • id: 8002639
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 18, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 750, 'label': '9000.o.1k2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 2]]]}
  • id: 8002640
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 19, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 750, 'label': '9000.o.1k3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 3]], [[1, 5]], [[1, 3]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 2]], [[1, 4]]]}
  • id: 8002642
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 20, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.b1.a1', 'kernel_order': 750, 'label': '9000.o.1k4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[1, 2]], [[1, 4]], [[-1, 2]]]}
  • id: 8002643
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 21, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 750, 'label': '9000.o.1l1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 3]], [[-1, 5]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]]]}
  • id: 8002644
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 22, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 750, 'label': '9000.o.1l2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 4]], [[1, 2]]]}
  • id: 8002645
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 23, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 750, 'label': '9000.o.1l3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 3]], [[1, 5]], [[1, 3]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 2]], [[-1, 4]]]}
  • id: 8002646
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 9000, 'counter': 24, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.a1.a1', 'kernel_order': 750, 'label': '9000.o.1l4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 4]], [[1, 2]]]}
  • id: 8002647
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 1500, 'label': '9000.o.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002648
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 750, 'label': '9000.o.2b', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002649
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 27, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 500, 'label': '9000.o.2c1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002650
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 28, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 500, 'label': '9000.o.2c2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002651
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 29, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 375, 'label': '9000.o.2d1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002653
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 30, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 375, 'label': '9000.o.2d2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002654
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 250, 'label': '9000.o.2e1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002655
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 250, 'label': '9000.o.2e2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002656
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 33, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 125, 'label': '9000.o.2f1', 'nt': [24, 65], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[-1, 3]], [[1, 5]], [[1, 3]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[2, 4]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[1, 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]]]}
  • id: 8002657
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 34, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 125, 'label': '9000.o.2f2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[1, 0]], [[1, 4]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002658
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 35, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 125, 'label': '9000.o.2f3', 'nt': [24, 65], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[1, 3]], [[-1, 5]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[2, 4]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[1, 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]]]}
  • id: 8002659
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 1500, 'counter': 36, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '72.27', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 125, 'label': '9000.o.2f4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[1, 0]], [[1, 4]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[-1, 3]], [[1, 1]], [[1, 3]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002660
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 450, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '20.3', 'image_order': 20, 'indicator': 1, 'kernel': '20.a1.a1', 'kernel_order': 450, 'label': '9000.o.4a', 'nt': [5, 3], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002661
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 450, 'counter': 38, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '40.12', 'image_order': 40, 'indicator': 1, 'kernel': '40.a1.a1', 'kernel_order': 225, 'label': '9000.o.4b', 'nt': [10, 5], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002662
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 450, 'counter': 39, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '60.6', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 150, 'label': '9000.o.4c1', 'nt': [15, 8], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[4, 1]], [[4, -1]], [[4, 1]], [[-1, 1]], [[-1, 1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[4, -1]], [[-1, -1]], [[-1, -1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002664
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 450, 'counter': 40, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '60.6', 'image_order': 60, 'indicator': 0, 'kernel': '60.a1.a1', 'kernel_order': 150, 'label': '9000.o.4c2', 'nt': [15, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[4, -1]], [[4, 1]], [[4, -1]], [[-1, -1]], [[-1, -1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[4, 1]], [[-1, 1]], [[-1, 1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002665
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 450, 'counter': 41, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '120.40', 'image_order': 120, 'indicator': 0, 'kernel': '120.b1.a1', 'kernel_order': 75, 'label': '9000.o.4d1', 'nt': [30, 26], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[4, 1]], [[4, -1]], [[4, 1]], [[-1, 1]], [[-1, 1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-4, -1]], [[1, -1]], [[1, -1]], [[-4, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002666
    {'center': '20.a1.a1', 'center_index': 20, 'center_order': 450, 'counter': 42, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '120.40', 'image_order': 120, 'indicator': 0, 'kernel': '120.b1.a1', 'kernel_order': 75, 'label': '9000.o.4d2', 'nt': [30, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[4, -1]], [[4, 1]], [[4, -1]], [[-1, -1]], [[-1, -1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-4, 1]], [[1, 1]], [[1, 1]], [[-4, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002667
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 75, 'counter': 43, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '120.36', 'image_order': 120, 'indicator': 1, 'kernel': '120.a1.a1', 'kernel_order': 75, 'label': '9000.o.8a', 'nt': [15, 11], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002668
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 75, 'counter': 44, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '360.126', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 25, 'label': '9000.o.8b1', 'nt': [30, 91], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[-4, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[8, 1]], [[8, -1]], [[8, 1]], [[-2, 1]], [[-2, 1]], [[8, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002669
    {'center': '120.a1.a1', 'center_index': 120, 'center_order': 75, 'counter': 45, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '360.126', 'image_order': 360, 'indicator': 0, 'kernel': '360.a1.a1', 'kernel_order': 25, 'label': '9000.o.8b2', 'nt': [30, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[-4, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[8, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[8, -1]], [[8, 1]], [[8, -1]], [[-2, -1]], [[-2, -1]], [[8, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002670
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 46, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '600.151', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 15, 'label': '9000.o.12a', 'nt': [15, 27], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 8002671
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 47, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '600.151', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 15, 'label': '9000.o.12b', 'nt': [15, 27], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002672
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 48, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.12c', 'nt': [15, 49], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002673
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 49, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.12d', 'nt': [15, 49], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002675
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 50, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.12e', 'nt': [15, 49], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002676
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 51, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.12f', 'nt': [15, 49], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002677
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 52, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '600.151', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 15, 'label': '9000.o.12g', 'nt': [30, 150], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002678
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 53, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '600.151', 'image_order': 600, 'indicator': 1, 'kernel': '600.a1.a1', 'kernel_order': 15, 'label': '9000.o.12h', 'nt': [30, 150], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 8002679
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 54, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.12i', 'nt': [30, 433], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002680
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 55, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.12j', 'nt': [30, 433], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002681
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 56, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.12k', 'nt': [30, 433], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002682
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 57, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.12l', 'nt': [30, 433], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002683
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 58, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '1800.569', 'image_order': 1800, 'indicator': 0, 'kernel': '1800.a1.a1', 'kernel_order': 5, 'label': '9000.o.12m1', 'nt': [45, 215], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 8002684
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 59, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '1800.569', 'image_order': 1800, 'indicator': 0, 'kernel': '1800.a1.a1', 'kernel_order': 5, 'label': '9000.o.12m2', 'nt': [45, 2], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 8002686
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 60, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '1800.569', 'image_order': 1800, 'indicator': 0, 'kernel': '1800.a1.a1', 'kernel_order': 5, 'label': '9000.o.12n1', 'nt': [45, 215], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[4, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002687
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 61, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '1800.569', 'image_order': 1800, 'indicator': 0, 'kernel': '1800.a1.a1', 'kernel_order': 5, 'label': '9000.o.12n2', 'nt': [45, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[4, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002688
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 62, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12o1', 'nt': [45, 473], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[-3, 1]], [[7, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[-3, 1]], [[2, 1]], [[-3, -1]], [[7, 1]], [[-3, -1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[4, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[4, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002689
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 63, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12o2', 'nt': [45, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[-3, -1]], [[7, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[-3, -1]], [[2, -1]], [[-3, 1]], [[7, -1]], [[-3, 1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[4, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[4, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002690
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 64, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12p1', 'nt': [45, 473], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[7, -1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[-3, 1]], [[7, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[4, 1]], [[4, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002691
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 65, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12p2', 'nt': [45, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[7, 1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[-3, -1]], [[7, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[4, -1]], [[4, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002692
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 66, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12q1', 'nt': [45, 473], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[7, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[7, -1]], [[2, 1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[4, -1]], [[4, 1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002693
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 67, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12q2', 'nt': [45, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[7, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[7, 1]], [[2, -1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[4, 1]], [[4, -1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002694
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 68, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12r1', 'nt': [45, 473], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[7, 1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[7, -1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002695
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 69, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12r2', 'nt': [45, 2], 'q_character': None, 'values': [[[12, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[7, -1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[7, 1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002697
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 70, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12s1', 'nt': [90, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[-3, 1]], [[7, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[-3, 1]], [[2, 1]], [[-3, -1]], [[7, 1]], [[-3, -1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[-4, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-4, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002698
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 71, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12s2', 'nt': [90, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[-3, -1]], [[7, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[-3, -1]], [[2, -1]], [[-3, 1]], [[7, -1]], [[-3, 1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[-4, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-4, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002699
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 72, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12t1', 'nt': [90, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[7, -1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[-3, 1]], [[7, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-4, 1]], [[-4, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002700
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 73, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12t2', 'nt': [90, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[7, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[7, 1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[-3, -1]], [[7, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-4, -1]], [[-4, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002701
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 74, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12u1', 'nt': [90, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[7, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[7, -1]], [[2, 1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-4, -1]], [[-4, 1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002702
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 75, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12u2', 'nt': [90, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[7, 0]], [[2, 0]], [[-3, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[7, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[7, 1]], [[2, -1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-4, 1]], [[-4, -1]], [[1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002703
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 76, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12v1', 'nt': [90, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[7, 1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[7, -1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002704
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 77, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.12v2', 'nt': [90, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[2, 0]], [[7, 0]], [[-3, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[7, -1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[7, 1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002705
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 78, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '1800.569', 'image_order': 1800, 'indicator': 0, 'kernel': '1800.a1.a1', 'kernel_order': 5, 'label': '9000.o.12w1', 'nt': [90, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[-3, 1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-4, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-4, 1]], [[0, 0]], [[0, 0]]]}
  • id: 8002706
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 79, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '1800.569', 'image_order': 1800, 'indicator': 0, 'kernel': '1800.a1.a1', 'kernel_order': 5, 'label': '9000.o.12w2', 'nt': [90, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[2, 1]], [[2, -1]], [[-3, -1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-4, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-4, -1]], [[0, 0]], [[0, 0]]]}
  • id: 8002708
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 80, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '1800.569', 'image_order': 1800, 'indicator': 0, 'kernel': '1800.a1.a1', 'kernel_order': 5, 'label': '9000.o.12x1', 'nt': [90, 0], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, -1]], [[12, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]]]}
  • id: 8002709
    {'center': '600.a1.a1', 'center_index': 600, 'center_order': 15, 'counter': 81, 'cyclotomic_n': 3, 'dim': 12, 'faithful': False, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '1800.569', 'image_order': 1800, 'indicator': 0, 'kernel': '1800.a1.a1', 'kernel_order': 5, 'label': '9000.o.12x2', 'nt': [90, 2], 'q_character': None, 'values': [[[12, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[12, 1]], [[12, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-3, 1]], [[-3, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]]]}
  • id: 8002710
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 82, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.24a', 'nt': [30, 435], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002711
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 83, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '3000.bf', 'image_order': 3000, 'indicator': 1, 'kernel': '3000.a1.a1', 'kernel_order': 3, 'label': '9000.o.24b', 'nt': [30, 435], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[24, 0]], [[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002712
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 84, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.24c1', 'nt': [90, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[24, -1]], [[24, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[-6, -1]], [[4, 1]], [[4, -1]], [[4, 1]], [[-6, -1]], [[-6, 1]], [[-6, 1]], [[-6, 1]], [[4, -1]], [[4, 1]], [[-6, -1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002713
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 85, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.24c2', 'nt': [90, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[24, 1]], [[24, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[-6, 1]], [[4, -1]], [[4, 1]], [[4, -1]], [[-6, 1]], [[-6, -1]], [[-6, -1]], [[-6, -1]], [[4, 1]], [[4, -1]], [[-6, 1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002714
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 86, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.24d1', 'nt': [90, 0], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[24, -1]], [[24, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, -1]], [[-6, 1]], [[4, -1]], [[-6, 1]], [[-6, -1]], [[4, 1]], [[-6, -1]], [[-6, 1]], [[4, 1]], [[4, 1]], [[4, -1]], [[-6, 1]], [[4, -1]], [[-6, -1]], [[4, 1]], [[4, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 8002715
    {'center': '3000.a1.a1', 'center_index': 3000, 'center_order': 3, 'counter': 87, 'cyclotomic_n': 3, 'dim': 24, 'faithful': True, 'field': [1, -1, 1], 'group': '9000.o', 'group_counter': 15, 'group_order': 9000, 'image': None, 'image_isoclass': '9000.o', 'image_order': 9000, 'indicator': 0, 'kernel': '9000.a1.a1', 'kernel_order': 1, 'label': '9000.o.24d2', 'nt': [90, 2], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[24, 1]], [[24, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[4, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-6, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[-6, -1]], [[4, 1]], [[-6, -1]], [[-6, 1]], [[4, -1]], [[-6, 1]], [[-6, -1]], [[4, -1]], [[4, -1]], [[4, 1]], [[-6, -1]], [[4, 1]], [[-6, 1]], [[4, -1]], [[4, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 68997716
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 9000, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '9000.o.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9000.o', 'subgroup_hash': 1735341798720924668, 'subgroup_order': 9000, 'subgroup_tex': 'C_5^3:(S_3\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 68997827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 4500, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4500.u', 'subgroup_hash': 3430076343012405519, 'subgroup_order': 4500, 'subgroup_tex': 'C_3\\times C_5^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 68997938
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 4500, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4500.o', 'subgroup_hash': 882038474055215773, 'subgroup_order': 4500, 'subgroup_tex': 'C_3\\times C_5^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 68998006
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 4500, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4500.l', 'subgroup_hash': 4257863390704883839, 'subgroup_order': 4500, 'subgroup_tex': 'C_5\\wr C_3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 68998017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': True, 'centralizer_order': 3, 'characteristic': True, 'core_order': 3000, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '9000.o.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': '3000.bf', 'subgroup_hash': 3629711919683738508, 'subgroup_order': 3000, 'subgroup_tex': 'C_5^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 68998028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1500, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3486932366726379732, 'subgroup_order': 3000, 'subgroup_tex': 'C_3\\times C_5^3:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 68998039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 2250, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', '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': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2250.m', 'subgroup_hash': 5021819265297054477, 'subgroup_order': 2250, 'subgroup_tex': 'C_3\\times C_5\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68998050
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 2250, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2250.j', 'subgroup_hash': 391427703906437627, 'subgroup_order': 2250, 'subgroup_tex': 'C_3\\times C_5^2:D_{15}', 'supersolvable': False, 'sylow': 0}
  • id: 68998061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 2250, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2250.g', 'subgroup_hash': 3638640786514561450, 'subgroup_order': 2250, 'subgroup_tex': 'C_3\\times C_5^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 68997717
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 450, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.5.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 5, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1800.569', 'subgroup_hash': 569, 'subgroup_order': 1800, 'subgroup_tex': 'C_5^2:(S_3\\times C_{12})', 'supersolvable': False, 'sylow': 0}
  • id: 68997728
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1500, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': 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': '1500.125', 'subgroup_hash': 125, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^3:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 68997739
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1500, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.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': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1500.138', 'subgroup_hash': 138, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68997750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1500, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.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': '1500.119', 'subgroup_hash': 119, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 68997761
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1500, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.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': '1500.115', 'subgroup_hash': 115, 'subgroup_order': 1500, 'subgroup_tex': 'C_5\\wr C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 68997772
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 750, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.153', 'subgroup_hash': 153, 'subgroup_order': 1500, 'subgroup_tex': 'C_{15}:D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 750, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.139', 'subgroup_hash': 139, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68997794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 500, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1500.119', 'subgroup_hash': 119, 'subgroup_order': 1500, 'subgroup_tex': 'C_5^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 68997805
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 1125, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 15, 'label': '9000.o.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1125.13', 'subgroup_hash': 13, 'subgroup_order': 1125, 'subgroup_tex': 'C_5^3:C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 68997816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 500, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '9000.o.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1000.168', 'subgroup_hash': 168, 'subgroup_order': 1000, 'subgroup_tex': 'C_5^3:(C_2\\times C_4)', 'supersolvable': True, 'sylow': 0}
  • id: 68997828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 450, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.93', 'subgroup_hash': 93, 'subgroup_order': 900, 'subgroup_tex': 'C_3\\times C_5^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 68997839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 225, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.91', 'subgroup_hash': 91, 'subgroup_order': 900, 'subgroup_tex': 'C_3\\times C_5^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 68997850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 225, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.10.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '900.89', 'subgroup_hash': 89, 'subgroup_order': 900, 'subgroup_tex': 'C_5^2:C_3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 68997861
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 750, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '750.26', 'subgroup_hash': 26, 'subgroup_order': 750, 'subgroup_tex': 'C_5\\wr S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68997872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 750, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', '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': '750.27', 'subgroup_hash': 27, 'subgroup_order': 750, 'subgroup_tex': 'C_5^2:D_{15}', 'supersolvable': False, 'sylow': 0}
  • id: 68997883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 750, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '750.34', 'subgroup_hash': 34, 'subgroup_order': 750, 'subgroup_tex': 'C_5^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68997894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 750, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.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': '750.30', 'subgroup_hash': 30, 'subgroup_order': 750, 'subgroup_tex': 'C_5^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 68997905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 375, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.32', 'subgroup_hash': 32, 'subgroup_order': 750, 'subgroup_tex': 'C_5^2:C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68997916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 375, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.33', 'subgroup_hash': 33, 'subgroup_order': 750, 'subgroup_tex': 'C_5^2:C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68997927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '750.30', 'subgroup_hash': 30, 'subgroup_order': 750, 'subgroup_tex': 'C_5^3:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 68997939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '600.185', 'subgroup_hash': 185, 'subgroup_order': 600, 'subgroup_tex': 'C_{30}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997950
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.15.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 15, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, '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: 68997961
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.15.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.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': 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': '600.157', 'subgroup_hash': 157, 'subgroup_order': 600, 'subgroup_tex': 'D_5^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68997972
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.15.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.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': 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': '600.157', 'subgroup_hash': 157, 'subgroup_order': 600, 'subgroup_tex': 'D_5^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68997983
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.15.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.c1.c1', 'outer_equivalence': False, 'perfect': False, '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': '600.157', 'subgroup_hash': 157, 'subgroup_order': 600, 'subgroup_tex': 'D_5^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68997994
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.15.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.c1.d1', 'outer_equivalence': False, 'perfect': False, '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': '600.157', 'subgroup_hash': 157, 'subgroup_order': 600, 'subgroup_tex': 'D_5^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68998002
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.15.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.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': 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': '600.157', 'subgroup_hash': 157, 'subgroup_order': 600, 'subgroup_tex': 'D_5^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68998003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 150, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.15.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '15.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '600.151', 'subgroup_hash': 151, 'subgroup_order': 600, 'subgroup_tex': 'C_5^2:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
  • id: 68998004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 500, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '500.48', 'subgroup_hash': 48, 'subgroup_order': 500, 'subgroup_tex': 'C_5^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68998005
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '500.51', 'subgroup_hash': 51, 'subgroup_order': 500, 'subgroup_tex': 'C_5:D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68998007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 250, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '500.49', 'subgroup_hash': 49, 'subgroup_order': 500, 'subgroup_tex': 'C_5^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68998008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 450, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '450.20', 'subgroup_hash': 20, 'subgroup_order': 450, 'subgroup_tex': 'C_3\\times C_5^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68998009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 225, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.20', 'subgroup_hash': 20, 'subgroup_order': 450, 'subgroup_tex': 'C_3\\times C_5^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68998010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 225, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '450.22', 'subgroup_hash': 22, 'subgroup_order': 450, 'subgroup_tex': 'C_3\\times C_5^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 68998011
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': True, 'core_order': 375, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '375.7', 'subgroup_hash': 7, 'subgroup_order': 375, 'subgroup_tex': 'C_5^2\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68998012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 375, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.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', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '375.6', 'subgroup_hash': 6, 'subgroup_order': 375, 'subgroup_tex': 'C_5\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 68998013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '375.6', 'subgroup_hash': 6, 'subgroup_order': 375, 'subgroup_tex': 'C_5\\wr C_3', 'supersolvable': False, 'sylow': 0}
  • id: 68998014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.25.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '25.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 25, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '360.126', 'subgroup_hash': 126, 'subgroup_order': 360, 'subgroup_tex': 'D_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68998015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.45', 'subgroup_hash': 45, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68998016
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68998018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68998019
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68998020
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.c1', 'outer_equivalence': False, 'perfect': False, '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': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68998021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.c1.d1', 'outer_equivalence': False, 'perfect': False, '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': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68998022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.36', 'subgroup_hash': 36, 'subgroup_order': 300, 'subgroup_tex': 'C_3\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68998023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 150, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.25', 'subgroup_hash': 25, 'subgroup_order': 300, 'subgroup_tex': 'C_5^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 68998024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, '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: 68998025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, '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: 68998026
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998027
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.i1.c1', 'outer_equivalence': False, 'perfect': False, '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': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.i1.d1', 'outer_equivalence': False, 'perfect': False, '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': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.30', 'subgroup_hash': 30, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.m1.c1', 'outer_equivalence': False, 'perfect': False, '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': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.m1.d1', 'outer_equivalence': False, 'perfect': False, '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': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.31', 'subgroup_hash': 31, 'subgroup_order': 300, 'subgroup_tex': 'C_{15}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.24', 'subgroup_hash': 24, 'subgroup_order': 300, 'subgroup_tex': 'C_5^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 68998043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.23', 'subgroup_hash': 23, 'subgroup_order': 300, 'subgroup_tex': 'C_5^2:C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 68998044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 25, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.30.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '30.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 30, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '300.24', 'subgroup_hash': 24, 'subgroup_order': 300, 'subgroup_tex': 'C_5^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 68998045
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 250, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '250.14', 'subgroup_hash': 14, 'subgroup_order': 250, 'subgroup_tex': 'C_5^3:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68998046
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 125, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '250.12', 'subgroup_hash': 12, 'subgroup_order': 250, 'subgroup_tex': 'D_5\\times C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68998047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 125, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '250.13', 'subgroup_hash': 13, 'subgroup_order': 250, 'subgroup_tex': 'C_5^2:C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68998048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 225, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '225.5', 'subgroup_hash': 5, 'subgroup_order': 225, 'subgroup_tex': 'C_5^2:C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 68998049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.45.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.47', 'subgroup_hash': 47, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998051
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 5, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.45.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.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': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.45.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.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': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998053
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.45.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.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': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.45.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.45.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 25, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.45.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '45.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': 45, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.50.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '50.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.26', 'subgroup_hash': 26, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 68998058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 15, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.50.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '50.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '180.20', 'subgroup_hash': 20, 'subgroup_order': 180, 'subgroup_tex': 'C_3^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68998059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.50.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '180.21', 'subgroup_hash': 21, 'subgroup_order': 180, 'subgroup_tex': 'C_{15}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68998060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 150, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.6', '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': '150.5', 'subgroup_hash': 5, 'subgroup_order': 150, 'subgroup_tex': 'C_5^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68998062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 15, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.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': '150.13', 'subgroup_hash': 13, 'subgroup_order': 150, 'subgroup_tex': 'C_5\\times C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68998063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 15, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.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': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68998064
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.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': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68998065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.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': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68998066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1.c1', 'outer_equivalence': False, 'perfect': False, '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': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68998067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 3, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.d1.d1', 'outer_equivalence': False, 'perfect': False, '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': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68998068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 75, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68998069
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 15, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68998070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68998071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997718
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.g1.c1', 'outer_equivalence': False, 'perfect': False, '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': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997719
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 3, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.g1.d1', 'outer_equivalence': False, 'perfect': False, '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': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997720
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 75, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.8', 'subgroup_hash': 8, 'subgroup_order': 150, 'subgroup_tex': 'D_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997721
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.5', 'subgroup_hash': 5, 'subgroup_order': 150, 'subgroup_tex': 'C_5^2:S_3', 'supersolvable': False, 'sylow': 0}
  • id: 68997722
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997723
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997724
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997725
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997726
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997727
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997729
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997730
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.n1.c1', 'outer_equivalence': False, 'perfect': False, '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': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997731
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.n1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.n1.d1', 'outer_equivalence': False, 'perfect': False, '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': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997732
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.9', 'subgroup_hash': 9, 'subgroup_order': 150, 'subgroup_tex': 'C_{15}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997733
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.6', 'subgroup_hash': 6, 'subgroup_order': 150, 'subgroup_tex': 'C_5^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 68997734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 25, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.60.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '60.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 60, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '150.6', 'subgroup_hash': 6, 'subgroup_order': 150, 'subgroup_tex': 'C_5^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 68997735
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': True, 'core_order': 125, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 5, 'label': '9000.o.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.27', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '125.5', 'subgroup_hash': 5, 'subgroup_order': 125, 'subgroup_tex': 'C_5^3', 'supersolvable': True, 'sylow': 5}
  • id: 68997736
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.75.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997737
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.75.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997738
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.75.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.75.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.b1.c1', 'outer_equivalence': False, 'perfect': False, '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': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.75.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.b1.d1', 'outer_equivalence': False, 'perfect': False, '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': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997742
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.75.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 75, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997743
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 5, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.75.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.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': 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': '120.36', 'subgroup_hash': 36, 'subgroup_order': 120, 'subgroup_tex': 'S_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997744
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.75.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '75.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '120.40', 'subgroup_hash': 40, 'subgroup_order': 120, 'subgroup_tex': 'C_6\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997746
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 5, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997747
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997748
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997749
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997751
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997752
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 25, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, '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: 68997754
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 5, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997755
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997757
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997758
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997760
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 25, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997763
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997764
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 5, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997765
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997766
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997768
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997769
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 25, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.90.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '90.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 90, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 15, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.100.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.6', 'subgroup_hash': 6, 'subgroup_order': 90, 'subgroup_tex': 'S_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997771
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 15, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.100.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.7', 'subgroup_hash': 7, 'subgroup_order': 90, 'subgroup_tex': 'C_3\\times D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 15, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.100.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '100.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '90.5', 'subgroup_hash': 5, 'subgroup_order': 90, 'subgroup_tex': 'C_3^2\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997774
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': True, 'core_order': 75, 'counter': 151, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.36', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times F_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': True, 'core_order': 75, 'counter': 152, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.40', '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': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '75.2', 'subgroup_hash': 2, 'subgroup_order': 75, 'subgroup_tex': 'C_5^2:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 68997776
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 15, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997777
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 15, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.120.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 3, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.120.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 3, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.120.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 3, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.120.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997781
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 3, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.120.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997782
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 3, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.120.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997784
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 3, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.120.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '120.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.3', 'subgroup_hash': 3, 'subgroup_order': 75, 'subgroup_tex': 'C_5\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 25, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.120.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 120, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '75.2', 'subgroup_hash': 2, 'subgroup_order': 75, 'subgroup_tex': 'C_5^2:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 68997786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '9000.o.125.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '125.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': 125, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68997787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997789
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997790
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.b1.c1', 'outer_equivalence': False, 'perfect': False, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.b1.d1', 'outer_equivalence': False, 'perfect': False, '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': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 5, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.8', 'subgroup_hash': 8, 'subgroup_order': 60, 'subgroup_tex': 'S_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997795
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.10', 'subgroup_hash': 10, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997796
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 15, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997797
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997798
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997799
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.g1.c1', 'outer_equivalence': False, 'perfect': False, '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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997800
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.g1.d1', 'outer_equivalence': False, 'perfect': False, '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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997801
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997802
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 150, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997803
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997804
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997806
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 15, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997807
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997808
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997809
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.l1.c1', 'outer_equivalence': False, 'perfect': False, '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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997810
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.l1.d1', 'outer_equivalence': False, 'perfect': False, '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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997811
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997812
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997813
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 5, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997814
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 5, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.7', 'subgroup_hash': 7, 'subgroup_order': 60, 'subgroup_tex': 'C_{15}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68997815
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 5, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.150.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '150.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '60.6', 'subgroup_hash': 6, 'subgroup_order': 60, 'subgroup_tex': 'C_3\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 5, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '180.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997818
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 5, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 75, 'characteristic': False, 'core_order': 25, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 5, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 25, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 5, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 5, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997840
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 25, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.180.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 180, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 15, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.200.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '45.2', 'subgroup_hash': 2, 'subgroup_order': 45, 'subgroup_tex': 'C_3\\times C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.225.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997845
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.225.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.225.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.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': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.225.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.225.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997849
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.225.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997851
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.225.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '225.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': 225, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997852
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.250.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '250.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': 250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68997853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.250.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '250.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': 250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68997854
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.250.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '250.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': 250, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 68997855
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 15, 'counter': 224, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.300.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 68997856
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 3, 'counter': 225, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.300.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 68997857
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 3, 'counter': 226, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.300.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.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': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68997858
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 3, 'counter': 227, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.300.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68997859
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 3, 'counter': 228, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.300.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68997860
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 3, 'counter': 229, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.300.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68997862
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 15, 'characteristic': False, 'core_order': 5, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.1', 'subgroup_hash': 1, 'subgroup_order': 30, 'subgroup_tex': 'C_5\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68997863
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 3, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997864
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.300.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '300.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
  • id: 68997865
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 15, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997866
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997867
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997868
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997869
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997870
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 3, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997871
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 5, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.3', 'subgroup_hash': 3, 'subgroup_order': 30, 'subgroup_tex': 'D_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997873
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 15, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997874
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997875
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997876
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997877
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997878
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997879
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997880
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997881
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997882
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 5, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997884
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 5, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.300.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 300, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.2', 'subgroup_hash': 2, 'subgroup_order': 30, 'subgroup_tex': 'C_3\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': True, 'core_order': 25, 'counter': 251, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '9000.o.360.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '360.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '360.126', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 126, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 360, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{15}:C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997886
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 5, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.360.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997887
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 5, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.360.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997888
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.360.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.360.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997890
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.360.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.360.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.360.e1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.e1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997893
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.360.e1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '360.e1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 360, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 68997895
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.375.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '375.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': 375, 'quotient_simple': None, '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: 68997896
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.375.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '375.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': 375, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68997897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997904
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 5, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997906
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997907
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997908
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997909
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997910
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997911
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997912
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997913
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997914
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 5, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997915
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997917
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997918
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.k1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997919
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.k1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.k1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997920
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997921
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.450.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '450.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 450, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997922
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 3, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.500.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '500.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': 500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68997923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.500.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '500.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': 500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68997924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.500.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '500.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': 500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 68997925
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 2250, 'characteristic': True, 'core_order': 15, 'counter': 288, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '9000.o.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': False, 'proper': True, 'quotient': '600.151', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 151, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 600, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_5^2:(C_4\\times S_3)', '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: 68997926
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 3, 'counter': 289, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997928
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 3, 'counter': 290, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.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': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997929
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 3, 'counter': 291, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997930
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 3, 'counter': 292, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997931
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 3, 'counter': 293, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997932
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 3, 'counter': 294, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997933
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 3, 'counter': 295, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997934
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 3, 'counter': 296, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997935
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 5, 'counter': 297, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997936
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 45, 'characteristic': False, 'core_order': 5, 'counter': 298, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.600.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '600.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 600, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
  • id: 68997937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.750.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '750.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': 750, 'quotient_simple': None, '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: 68997940
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.750.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '750.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': 750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 68997941
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 301, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.750.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '750.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': 750, 'quotient_simple': None, '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: 68997942
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 302, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.750.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '750.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': 750, 'quotient_simple': None, '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: 68997943
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 303, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.750.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '750.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 750, 'quotient_simple': None, '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: 68997944
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.750.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '750.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 750, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68997945
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 305, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.750.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '750.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 750, 'quotient_simple': None, '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: 68997946
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 5, 'counter': 306, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.900.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997947
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.900.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997948
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 308, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.900.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997949
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 309, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.900.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997951
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 310, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.900.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997952
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 311, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.900.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997953
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 150, 'characteristic': False, 'core_order': 1, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997954
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 313, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.900.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '900.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 68997955
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 5, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997956
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997957
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997958
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997959
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.g1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997960
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 30, 'characteristic': False, 'core_order': 1, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997962
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 5, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997963
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997964
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997965
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997966
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.j1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.j1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997967
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997968
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997969
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997970
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.900.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '900.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 900, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 68997971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 3, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '9000.o.1000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1000.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': 1000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 3}
  • id: 68997973
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '9000.o.1125.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1125.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': 1125, 'quotient_simple': 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: 68997974
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 600, 'characteristic': False, 'core_order': 3, 'counter': 331, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1500.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1500.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': 1500, 'quotient_simple': 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: 68997975
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 60, 'characteristic': False, 'core_order': 1, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.1500.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1500.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': 1500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68997976
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 3, 'counter': 333, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1500.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1500.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': 1500, 'quotient_simple': 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: 68997977
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.1500.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1500.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': 1500, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 68997978
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 335, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1500.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1500.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1500, 'quotient_simple': 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: 68997979
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 336, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1500.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1500.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1500, 'quotient_simple': 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: 68997980
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 337, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1500.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1500.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1500, 'quotient_simple': 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: 68997981
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 2250, 'characteristic': True, 'core_order': 5, 'counter': 338, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '9000.o.1800.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1800.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1800.569', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 569, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1800, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_5^2:(S_3\\times C_{12})', '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: 68997982
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 1, 'counter': 339, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1800.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 68997984
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 1, 'counter': 340, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1800.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 68997985
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 1, 'counter': 341, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1800.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 68997986
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 1, 'counter': 342, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1800.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 68997987
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 1, 'counter': 343, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1800.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 68997988
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 750, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1800.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 68997989
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1800.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 68997990
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 375, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.1800.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1800.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 68997991
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '9000.o.2250.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2250.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': 2250, 'quotient_simple': 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: 68997992
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.2250.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2250.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': 2250, 'quotient_simple': 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: 68997993
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 349, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.2250.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2250.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': 2250, 'quotient_simple': 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: 68997995
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': True, 'central_factor': False, 'centralizer_order': 9000, 'characteristic': True, 'core_order': 3, 'counter': 350, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '9000.o.3000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '3000.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3000.bf', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3629711919683738508, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 3000, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_5^3:(C_4\\times S_3)', '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': 0}
  • id: 68997996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 351, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.3000.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3000.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': 3000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 68997997
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 180, 'characteristic': False, 'core_order': 1, 'counter': 352, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.3000.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3000.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': 3000, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 68997998
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 600, 'characteristic': False, 'core_order': 1, 'counter': 353, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.4500.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4500.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': 4500, '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: 68997999
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 120, 'characteristic': False, 'core_order': 1, 'counter': 354, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.4500.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4500.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': 4500, '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: 68998000
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 355, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '9000.o.4500.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4500.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': 4500, '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: 68998001
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '9000.o', 'ambient_counter': 15, 'ambient_order': 9000, 'ambient_tex': 'C_5^3:(S_3\\times C_{12})', 'central': True, 'central_factor': False, 'centralizer_order': 9000, 'characteristic': True, 'core_order': 1, 'counter': 356, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '9000.o.9000.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9000.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '9000.o', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1735341798720924668, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 9000, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_5^3:(S_3\\times C_{12})', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 68997716
    {'ambient': '9000.o', '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': '3000.a1.a1', 'complements': ['9000.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '3.b1.a1', '5.a1.a1', '25.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6445, 5584, 2399, 4220, 2953, 5776, 1988, 6221], 'generators': [3, 1200, 5760, 4, 24, 1800, 60, 6], 'label': '9000.o.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '3000.bf', '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': '3000.bf'}
  • id: 68997717
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '15.d1.a1', '15.e1.a1', '125.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6445, -1, 2399, -1, 2792, -1, 1820, -1], 'generators': [3, 5760, 4, 6, 60, 1800, 1200], 'label': '9000.o.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': '3000.bf', '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': '600.151'}
  • id: 68997718
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.c1.c1'], 'contains': ['120.f1.c1', '180.f1.c1', '300.f1.a1', '300.h1.d1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4885, -1, 8489, -1, 4079, -1, 3745, -1], 'generators': [114, 5760, 1464, 4], 'label': '9000.o.60.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '60.g1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.c1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997719
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.c1.d1'], 'contains': ['120.f1.d1', '180.f1.d1', '300.f1.a1', '300.h1.c1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4885, -1, 8104, -1, 4079, -1, 3628, -1], 'generators': [114, 5760, 1104, 4], 'label': '9000.o.60.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '60.g1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.d1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997720
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '20.b1.a1', '30.d1.a1'], 'contains': ['120.a1.a1', '180.g1.a1', '300.f1.a1', '300.i1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3495, -1, 9365, -1, 3388, -1, 2556, -1], 'generators': [114, 1800, 360, 4], 'label': '9000.o.60.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '60.h1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.h1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997721
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.b1.a1', '30.e1.a1'], 'contains': ['120.b1.a1', '180.g1.a1', '1500.d1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [818, -1, 9028, -1, 690, -1, 714, -1], 'generators': [114, 3960, 1800, 1200], 'label': '9000.o.60.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.i1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.i1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68997722
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.a1.a1'], 'contains': ['120.c1.a1', '180.h1.a1', '300.g1.a1', '300.h1.a1', '300.h1.b1', '300.h1.c1', '300.h1.d1', '300.i1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2374, -1, 6818, -1, 3735, -1, 4097, -1], 'generators': [114, 24, 360, 4], 'label': '9000.o.60.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '60.j1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.j1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997723
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '30.a1.a1', '30.f1.a1', '30.k1.a1'], 'contains': ['120.c1.a1', '180.i1.a1', '300.k1.a1', '300.l1.a1', '300.l1.b1', '300.l1.c1', '300.l1.d1', '300.m1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4502, -1, 4257, -1, 6588, -1, 6333, -1], 'generators': [6, 24, 360, 4], 'label': '9000.o.60.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.k1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.k1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997724
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '30.b1.a1', '30.g1.a1', '30.l1.a1'], 'contains': ['120.d1.a1', '180.j1.a1', '300.k1.a1', '300.n1.a1', '300.o1.a1', '300.o1.b1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5357, -1, 4739, -1, 6297, -1, 5497, -1], 'generators': [6, 24, 3960, 4], 'label': '9000.o.60.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.l1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.l1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997725
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '30.h1.a1'], 'contains': ['120.e1.a1', '180.k1.a1', '300.l1.a1', '300.l1.d1', '300.m1.a1', '300.o1.a1', '300.o1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5973, -1, 3802, -1, 6936, -1, 6213, -1], 'generators': [6, 1824, 360, 4], 'label': '9000.o.60.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.h1.a1', 'old_label': '60.m1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997726
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '30.h1.b1'], 'contains': ['120.e1.b1', '180.k1.b1', '300.l1.b1', '300.l1.c1', '300.m1.a1', '300.o1.a1', '300.o1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5973, -1, 3714, -1, 6936, -1, 5855, -1], 'generators': [6, 3624, 360, 4], 'label': '9000.o.60.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.h1.b1', 'old_label': '60.m1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.m1.b1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997727
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '30.c1.a1', '30.i1.a1', '30.m1.a1'], 'contains': ['120.f1.a1', '180.l1.a1', '300.l1.a1', '300.l1.c1', '300.n1.a1', '300.o1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7806, -1, 5077, -1, 6762, -1, 6094, -1], 'generators': [6, 7224, 3960, 4], 'label': '9000.o.60.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '60.n1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997728
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.d1.a1', '18.b1.a1', '30.e1.a1', '150.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1851, 4214, 5751, 5353, 1798, 4509, 1202, 4485], 'generators': [6, 1800, 1200, 24, 60, 7560], 'label': '9000.o.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.b1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '9000.o', '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': '3000.bf'}
  • id: 68997729
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '30.c1.b1', '30.i1.b1', '30.m1.b1'], 'contains': ['120.f1.b1', '180.l1.b1', '300.l1.a1', '300.l1.b1', '300.n1.a1', '300.o1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7806, -1, 5987, -1, 6762, -1, 5616, -1], 'generators': [6, 5424, 3960, 4], 'label': '9000.o.60.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '60.n1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997730
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '30.c1.c1', '30.i1.c1', '30.m1.c1'], 'contains': ['120.f1.c1', '180.l1.c1', '300.l1.b1', '300.l1.d1', '300.n1.a1', '300.o1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7806, -1, 5686, -1, 6762, -1, 5974, -1], 'generators': [6, 1824, 3960, 4], 'label': '9000.o.60.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '60.n1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997731
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '30.c1.d1', '30.i1.d1', '30.m1.d1'], 'contains': ['120.f1.d1', '180.l1.d1', '300.l1.c1', '300.l1.d1', '300.n1.a1', '300.o1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7806, -1, 4837, -1, 6762, -1, 5736, -1], 'generators': [6, 3624, 3960, 4], 'label': '9000.o.60.n1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '60.n1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.n1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997732
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.c1.a1', '30.d1.a1', '30.j1.a1', '30.n1.a1'], 'contains': ['120.a1.a1', '180.m1.a1', '300.m1.a1', '300.n1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5195, -1, 5819, -1, 6123, -1, 4531, -1], 'generators': [6, 360, 1800, 4], 'label': '9000.o.60.o1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.o1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.o1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68997733
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '20.c1.a1', '30.e1.a1', '30.o1.a1', '30.p1.a1'], 'contains': ['120.b1.a1', '180.m1.a1', '1500.f1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2126, -1, 5573, -1, 2092, -1, 1102, -1], 'generators': [6, 360, 1800, 1200], 'label': '9000.o.60.p1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '60.p1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.p1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68997734
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '20.c1.a1', '30.q1.a1'], 'contains': ['120.g1.a1', '180.m1.a1', '1500.g1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [2658, -1, 2193, -1, 1730, -1, 993, -1], 'generators': [6, 360, 1800, 1204], 'label': '9000.o.60.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '60.q1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.q1.a1', 'subgroup_fusion': None, 'weyl_group': '300.24'}
  • id: 68997735
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': ['125.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '36.a1.a1', '36.b1.a1', '36.c1.a1'], 'contains': ['360.a1.a1', '360.b1.a1', '360.c1.a1', '360.d1.a1', '360.d1.b1', '360.e1.a1', '360.e1.b1', '360.e1.c1', '360.e1.d1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2788, 4609, 8786, 5127, 4084, 5022, 2026, 4985], 'generators': [24, 1800, 360], 'label': '9000.o.72.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1'], 'normal_contains': ['360.a1.a1', '1800.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': '24.5', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 68997736
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '75.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.b1.a1', '25.a1.a1'], 'contains': ['150.a1.a1', '150.f1.a1', '150.k1.a1', '225.a1.a1', '375.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6695, -1, 2302, -1, 7907, -1, 7589, -1], 'generators': [1203, 4, 6, 60, 24], 'label': '9000.o.75.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '75.a1.a1', 'projective_image': '3000.bf', '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': '20.3'}
  • id: 68997737
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '75.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.c1.a1'], 'contains': ['150.b1.a1', '150.g1.a1', '150.l1.a1', '225.b1.a1', '375.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9779, -1, 3126, -1, 8813, -1, 8803, -1], 'generators': [1203, 4, 6, 60, 384], 'label': '9000.o.75.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '75.b1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997738
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '75.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.c1.b1'], 'contains': ['150.b1.b1', '150.g1.b1', '150.l1.b1', '225.b1.b1', '375.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9779, -1, 3237, -1, 8813, -1, 8315, -1], 'generators': [1203, 4, 6, 60, 744], 'label': '9000.o.75.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '75.b1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997739
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': ['1500.b1.a1', '1500.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '18.a1.a1', '30.f1.a1', '30.g1.a1', '30.h1.a1', '30.h1.b1', '30.i1.a1', '30.i1.b1', '30.i1.c1', '30.i1.d1', '30.j1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7283, 9259, 1535, 843, 7173, 9264, 6833, 9260], 'generators': [5733, 1800, 102, 24, 4, 360], 'label': '9000.o.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.c1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '3000.bf', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3000.bf'}
  • id: 68997740
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '75.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.c1.d1'], 'contains': ['150.b1.c1', '150.g1.c1', '150.l1.c1', '225.b1.c1', '375.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9779, -1, 2494, -1, 8813, -1, 8478, -1], 'generators': [1203, 4, 6, 60, 1104], 'label': '9000.o.75.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '75.b1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.b1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997741
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '75.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.c1.c1'], 'contains': ['150.b1.d1', '150.g1.d1', '150.l1.d1', '225.b1.d1', '375.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9779, -1, 2664, -1, 8813, -1, 8706, -1], 'generators': [1203, 4, 6, 60, 1464], 'label': '9000.o.75.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '75.b1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.b1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997742
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '75.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '15.d1.a1'], 'contains': ['150.c1.a1', '150.h1.a1', '150.m1.a1', '225.c1.a1', '375.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8286, -1, 2151, -1, 8380, -1, 8033, -1], 'generators': [1203, 4, 6, 60, 360], 'label': '9000.o.75.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '75.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997743
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '75.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '25.a1.a1'], 'contains': ['150.d1.a1', '150.o1.a1', '150.p1.a1', '225.a1.a1', '375.b1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6304, -1, 872, -1, 3028, -1, 2044, -1], 'generators': [3, 6, 1200, 60, 24], 'label': '9000.o.75.d1.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.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 68997744
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '75.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.b1.a1', '15.c1.a1', '15.c1.b1', '15.c1.c1', '15.c1.d1', '15.d1.a1'], 'contains': ['150.e1.a1', '150.i1.a1', '150.n1.a1', '225.d1.a1', '375.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9286, -1, 3035, -1, 8239, -1, 7818, -1], 'generators': [1203, 4, 6, 60, 5760], 'label': '9000.o.75.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '75.e1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '75.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997745
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.a1.a1', '45.a1.a1'], 'contains': ['180.a1.a1', '180.h1.a1', '180.i1.a1', '450.a1.a1', '450.b1.a1', '450.b1.b1', '450.b1.c1', '450.b1.d1', '450.c1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4036, -1, 5194, -1, 5720, -1, 5377, -1], 'generators': [6, 24, 360, 60], 'label': '9000.o.90.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '90.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.a1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997746
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.b1.a1', '45.b1.a1'], 'contains': ['180.b1.a1', '180.e1.a1', '180.j1.a1', '450.a1.a1', '450.d1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3602, -1, 6101, -1, 5305, -1, 4344, -1], 'generators': [6, 24, 5760, 60], 'label': '9000.o.90.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '90.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997747
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.c1.a1', '45.c1.a1'], 'contains': ['180.c1.a1', '180.f1.a1', '180.l1.a1', '450.b1.a1', '450.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6012, -1, 6269, -1, 5850, -1, 4799, -1], 'generators': [6, 3624, 5760, 60], 'label': '9000.o.90.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '90.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997748
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.c1.b1', '45.c1.b1'], 'contains': ['180.c1.b1', '180.f1.b1', '180.l1.b1', '450.b1.b1', '450.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6012, -1, 6703, -1, 5850, -1, 4621, -1], 'generators': [6, 7224, 5760, 60], 'label': '9000.o.90.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '90.c1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997749
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.c1.c1', '45.c1.c1'], 'contains': ['180.c1.c1', '180.f1.c1', '180.l1.c1', '450.b1.d1', '450.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6012, -1, 6512, -1, 5850, -1, 4739, -1], 'generators': [6, 5424, 5760, 60], 'label': '9000.o.90.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '90.c1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997750
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': ['1500.a1.a1', '1500.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '18.a1.a1', '30.o1.a1', '150.o1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5665, 7680, 1042, 2355, 2665, 7945, 1755, 7936], 'generators': [5733, 1800, 102, 24, 1200, 360], 'label': '9000.o.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.d1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '9000.o', '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': '3000.bf'}
  • id: 68997751
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.c1.d1', '45.c1.d1'], 'contains': ['180.c1.d1', '180.f1.d1', '180.l1.d1', '450.b1.c1', '450.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6012, -1, 6185, -1, 5850, -1, 4680, -1], 'generators': [6, 1824, 5760, 60], 'label': '9000.o.90.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '90.c1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.c1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997752
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '30.d1.a1', '30.e1.a1', '45.d1.a1'], 'contains': ['180.d1.a1', '180.g1.a1', '180.m1.a1', '450.c1.a1', '450.d1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4232, -1, 6597, -1, 5218, -1, 4187, -1], 'generators': [6, 360, 1800, 60], 'label': '9000.o.90.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '90.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.d1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997753
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.f1.a1', '45.a1.a1'], 'contains': ['180.i1.a1', '450.e1.a1', '450.f1.a1', '450.f1.b1', '450.f1.c1', '450.f1.d1', '450.g1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6854, -1, 857, -1, 7879, -1, 8028, -1], 'generators': [5733, 24, 360, 102], 'label': '9000.o.90.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '90.e1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.e1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997754
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.g1.a1', '45.b1.a1'], 'contains': ['180.j1.a1', '450.e1.a1', '450.h1.a1', '450.i1.a1', '450.i1.b1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8466, -1, 987, -1, 7481, -1, 7076, -1], 'generators': [5733, 24, 3960, 102], 'label': '9000.o.90.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '90.f1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.f1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997755
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.h1.a1'], 'contains': ['180.k1.a1', '450.f1.a1', '450.f1.d1', '450.g1.a1', '450.i1.a1', '450.i1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8244, -1, 403, -1, 8114, -1, 7624, -1], 'generators': [5733, 1824, 360, 102], 'label': '9000.o.90.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.h1.a1', 'old_label': '90.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.g1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997756
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.h1.b1'], 'contains': ['180.k1.b1', '450.f1.b1', '450.f1.c1', '450.g1.a1', '450.i1.a1', '450.i1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8244, -1, 243, -1, 8114, -1, 7543, -1], 'generators': [5733, 3624, 360, 102], 'label': '9000.o.90.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.h1.b1', 'old_label': '90.g1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.g1.b1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997757
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.i1.a1', '45.c1.a1'], 'contains': ['180.l1.a1', '450.f1.a1', '450.f1.c1', '450.h1.a1', '450.i1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9149, -1, 2312, -1, 7997, -1, 7947, -1], 'generators': [5733, 7224, 3960, 102], 'label': '9000.o.90.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '90.h1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.h1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997758
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.i1.b1', '45.c1.b1'], 'contains': ['180.l1.b1', '450.f1.a1', '450.f1.b1', '450.h1.a1', '450.i1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9149, -1, 2433, -1, 7997, -1, 7704, -1], 'generators': [5733, 5424, 3960, 102], 'label': '9000.o.90.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '90.h1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.h1.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997759
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.i1.c1', '45.c1.c1'], 'contains': ['180.l1.c1', '450.f1.b1', '450.f1.d1', '450.h1.a1', '450.i1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9149, -1, 1747, -1, 7997, -1, 7866, -1], 'generators': [5733, 1824, 3960, 102], 'label': '9000.o.90.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '90.h1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.h1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997760
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.i1.d1', '45.c1.d1'], 'contains': ['180.l1.d1', '450.f1.c1', '450.f1.d1', '450.h1.a1', '450.i1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9149, -1, 1564, -1, 7997, -1, 7785, -1], 'generators': [5733, 3624, 3960, 102], 'label': '9000.o.90.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '90.h1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.h1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997761
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': ['1500.a1.a1', '1500.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.d1.a1', '18.c1.a1', '30.p1.a1', '150.p1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6817, 5391, 3903, 3590, 3601, 5491, 2370, 6855], 'generators': [3, 1800, 1200, 24, 6, 5760], 'label': '9000.o.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3000.bf'}
  • id: 68997762
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '30.j1.a1', '30.o1.a1', '30.q1.a1', '45.d1.a1'], 'contains': ['180.m1.a1', '450.g1.a1', '450.h1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7039, -1, 698, -1, 7082, -1, 6513, -1], 'generators': [5733, 360, 1800, 102], 'label': '9000.o.90.i1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '90.i1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.i1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68997763
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.k1.a1', '45.a1.a1'], 'contains': ['180.i1.a1', '450.j1.a1', '450.k1.a1', '450.k1.b1', '450.k1.c1', '450.k1.d1', '450.l1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7963, -1, 2900, -1, 9715, -1, 9966, -1], 'generators': [3, 24, 7560, 6], 'label': '9000.o.90.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '90.j1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.j1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997764
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.l1.a1', '45.b1.a1'], 'contains': ['180.j1.a1', '450.j1.a1', '450.m1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7471, -1, 3508, -1, 9328, -1, 8294, -1], 'generators': [3, 24, 2160, 6], 'label': '9000.o.90.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '90.k1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.k1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997765
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.m1.a1', '45.c1.a1'], 'contains': ['180.l1.a1', '450.k1.a1', '450.m1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9619, -1, 3392, -1, 9822, -1, 9700, -1], 'generators': [3, 1104, 2160, 6], 'label': '9000.o.90.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '90.l1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.l1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997766
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.m1.b1', '45.c1.b1'], 'contains': ['180.l1.b1', '450.k1.b1', '450.m1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9619, -1, 4003, -1, 9822, -1, 9312, -1], 'generators': [3, 384, 2160, 6], 'label': '9000.o.90.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '90.l1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.l1.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997767
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.m1.c1', '45.c1.c1'], 'contains': ['180.l1.c1', '450.k1.d1', '450.m1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9619, -1, 3145, -1, 9822, -1, 9635, -1], 'generators': [3, 744, 2160, 6], 'label': '9000.o.90.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '90.l1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.l1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997768
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.m1.d1', '45.c1.d1'], 'contains': ['180.l1.d1', '450.k1.c1', '450.m1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9619, -1, 3460, -1, 9822, -1, 9474, -1], 'generators': [3, 1464, 2160, 6], 'label': '9000.o.90.l1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '90.l1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.l1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997769
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '90.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '30.n1.a1', '30.p1.a1', '45.d1.a1'], 'contains': ['180.m1.a1', '450.l1.a1', '450.m1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8714, -1, 3935, -1, 9233, -1, 8358, -1], 'generators': [3, 3960, 1800, 6], 'label': '9000.o.90.m1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '90.m1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '90.m1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997770
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '50.a1.a1'], 'contains': ['200.a1.a1', '300.a1.a1', '300.d1.a1', '500.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [340, -1, 8024, -1, 1068, -1, 589, -1], 'generators': [60, 24, 1200, 4], 'label': '9000.o.100.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '100.a1.a1', 'projective_image': '3000.bf', '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': '24.5'}
  • id: 68997771
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '100.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '50.a1.a1'], 'contains': ['200.a1.a1', '300.g1.a1', '300.j1.a1', '500.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [614, -1, 7919, -1, 311, -1, 840, -1], 'generators': [114, 1200, 24, 4], 'label': '9000.o.100.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '100.b1.a1', 'projective_image': '3000.bf', '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': '120.36'}
  • id: 68997772
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '12.e1.a1', '12.f1.a1', '18.b1.a1', '30.a1.a1', '30.b1.a1', '30.c1.a1', '30.c1.b1', '30.c1.c1', '30.c1.d1', '30.d1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4632, -1, 6067, -1, 5370, -1, 4573, -1], 'generators': [6, 1800, 4, 24, 60, 360], 'label': '9000.o.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.e1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.168'}
  • id: 68997773
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '100.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '50.a1.a1', '50.b1.a1', '50.c1.a1'], 'contains': ['200.a1.a1', '300.k1.a1', '300.p1.a1', '300.q1.a1', '500.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [2504, -1, 4924, -1, 1911, -1, 1393, -1], 'generators': [6, 1200, 24, 4], 'label': '9000.o.100.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '100.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.c1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997774
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': ['75.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.e1.a1', '60.h1.a1', '60.o1.a1'], 'contains': ['360.a1.a1', '600.c1.a1', '600.d1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1977, 3584, 9618, 6108, 3528, 4121, 1875, 4080], 'generators': [4, 1800, 360], 'label': '9000.o.120.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1'], 'normal_contains': ['360.a1.a1', '3000.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': '24.5', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 68997775
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': ['75.a1.a1', '75.b1.a1', '75.b1.b1', '75.b1.c1', '75.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.a1.a1', '60.a1.a1', '60.i1.a1', '60.p1.a1'], 'contains': ['360.a1.a1', '3000.b1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [792, 2373, 9299, 7268, 1299, 3007, 463, 2962], 'generators': [1200, 1800, 7560], 'label': '9000.o.120.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': ['24.b1.a1', '40.a1.a1', '60.a1.a1'], 'normal_contains': ['360.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': '8.2', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68997776
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.b1.a1', '60.j1.a1', '60.k1.a1'], 'contains': ['360.b1.a1', '600.a1.a1', '600.b1.a1', '600.b1.b1', '600.b1.c1', '600.b1.d1', '600.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1706, -1, 7288, -1, 4758, -1, 4421, -1], 'generators': [4, 360, 24], 'label': '9000.o.120.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997777
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.c1.a1', '60.f1.a1', '60.l1.a1'], 'contains': ['360.c1.a1', '600.a1.a1', '600.d1.a1', '600.e1.a1', '600.e1.b1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2729, -1, 7804, -1, 4446, -1, 2310, -1], 'generators': [4, 3960, 24], 'label': '9000.o.120.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.d1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997778
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.m1.a1'], 'contains': ['360.d1.a1', '600.b1.a1', '600.b1.d1', '600.c1.a1', '600.e1.a1', '600.e1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3889, -1, 7076, -1, 5923, -1, 4241, -1], 'generators': [4, 360, 1824], 'label': '9000.o.120.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '120.e1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997779
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.m1.b1'], 'contains': ['360.d1.b1', '600.b1.b1', '600.b1.c1', '600.c1.a1', '600.e1.a1', '600.e1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3889, -1, 6944, -1, 5923, -1, 3506, -1], 'generators': [4, 360, 3624], 'label': '9000.o.120.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '120.e1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997780
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.d1.a1', '60.g1.a1', '60.n1.a1'], 'contains': ['360.e1.a1', '600.b1.a1', '600.b1.c1', '600.d1.a1', '600.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4567, -1, 8455, -1, 5333, -1, 3837, -1], 'generators': [4, 3960, 7224], 'label': '9000.o.120.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.f1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997781
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.d1.b1', '60.g1.b1', '60.n1.b1'], 'contains': ['360.e1.b1', '600.b1.a1', '600.b1.b1', '600.d1.a1', '600.e1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4567, -1, 9512, -1, 5333, -1, 3014, -1], 'generators': [4, 3960, 5424], 'label': '9000.o.120.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.f1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997782
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.d1.c1', '60.g1.c1', '60.n1.c1'], 'contains': ['360.e1.c1', '600.b1.b1', '600.b1.d1', '600.d1.a1', '600.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4567, -1, 9086, -1, 5333, -1, 3623, -1], 'generators': [4, 3960, 1824], 'label': '9000.o.120.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.f1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.c1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997783
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '18.c1.a1', '30.k1.a1', '30.l1.a1', '30.m1.a1', '30.m1.b1', '30.m1.c1', '30.m1.d1', '30.n1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8197, -1, 4181, -1, 9056, -1, 9045, -1], 'generators': [3, 1800, 6, 24, 4, 3960], 'label': '9000.o.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.f1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.168'}
  • id: 68997784
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '60.d1.d1', '60.g1.d1', '60.n1.d1'], 'contains': ['360.e1.d1', '600.b1.c1', '600.b1.d1', '600.d1.a1', '600.e1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4567, -1, 8329, -1, 5333, -1, 3194, -1], 'generators': [4, 3960, 3624], 'label': '9000.o.120.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '120.f1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.f1.d1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997785
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '120.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.a1.a1', '60.q1.a1'], 'contains': ['360.a1.a1', '3000.c1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1089, -1, 6262, -1, 838, -1, 327, -1], 'generators': [1204, 1800, 7560], 'label': '9000.o.120.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '120.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.g1.a1', 'subgroup_fusion': None, 'weyl_group': '300.24'}
  • id: 68997786
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '125.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '750.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '25.a1.a1'], 'contains': ['250.a1.a1', '250.b1.a1', '250.c1.a1', '375.a1.a1', '375.b1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [6641, -1, 466, -1, 2874, -1, 1911, -1], 'generators': [3, 1200, 60, 4, 6], 'label': '9000.o.125.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '125.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '125.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997787
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.b1.a1', '50.a1.a1', '75.a1.a1'], 'contains': ['300.a1.a1', '300.g1.a1', '300.k1.a1', '450.a1.a1', '750.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3419, -1, 5921, -1, 5104, -1, 4265, -1], 'generators': [6, 4, 24, 60], 'label': '9000.o.150.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.a1.a1', 'projective_image': '3000.bf', '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': '20.3'}
  • id: 68997788
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.a1', '75.b1.a1'], 'contains': ['300.b1.a1', '300.h1.a1', '300.l1.a1', '450.b1.a1', '750.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6442, -1, 5809, -1, 5965, -1, 5269, -1], 'generators': [6, 4, 384, 60], 'label': '9000.o.150.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '150.b1.a1', 'projective_image': '3000.bf', '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': '20.3'}
  • id: 68997789
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.b1', '75.b1.b1'], 'contains': ['300.b1.b1', '300.h1.b1', '300.l1.b1', '450.b1.b1', '750.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6442, -1, 5573, -1, 5965, -1, 4975, -1], 'generators': [6, 4, 744, 60], 'label': '9000.o.150.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '150.b1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997790
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.d1', '75.b1.c1'], 'contains': ['300.b1.c1', '300.h1.c1', '300.l1.c1', '450.b1.c1', '750.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6442, -1, 5481, -1, 5965, -1, 5073, -1], 'generators': [6, 4, 1104, 60], 'label': '9000.o.150.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '150.b1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.b1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997791
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.c1.c1', '75.b1.d1'], 'contains': ['300.b1.d1', '300.h1.d1', '300.l1.d1', '450.b1.d1', '750.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6442, -1, 5718, -1, 5965, -1, 5171, -1], 'generators': [6, 4, 1464, 60], 'label': '9000.o.150.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '150.b1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.b1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997792
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '30.d1.a1', '75.c1.a1'], 'contains': ['300.c1.a1', '300.i1.a1', '300.m1.a1', '450.c1.a1', '750.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4257, -1, 5645, -1, 5562, -1, 4877, -1], 'generators': [6, 4, 360, 60], 'label': '9000.o.150.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '150.c1.a1', 'projective_image': '3000.bf', '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': '20.3'}
  • id: 68997793
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '50.a1.a1', '75.d1.a1'], 'contains': ['300.d1.a1', '300.j1.a1', '300.p1.a1', '450.a1.a1', '750.b1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [1358, -1, 5349, -1, 1521, -1, 1288, -1], 'generators': [6, 1200, 24, 60], 'label': '9000.o.150.d1.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.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.d1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 68997794
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.g1.a1', '18.a1.a1', '30.q1.a1', '150.q1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6031, -1, 877, -1, 2255, -1, 1474, -1], 'generators': [5733, 1800, 102, 24, 1204, 360], 'label': '9000.o.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '6.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1500.119'}
  • id: 68997795
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '30.c1.a1', '30.c1.b1', '30.c1.c1', '30.c1.d1', '30.d1.a1', '75.e1.a1'], 'contains': ['300.e1.a1', '300.f1.a1', '300.n1.a1', '450.d1.a1', '750.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5636, -1, 6433, -1, 5419, -1, 4423, -1], 'generators': [6, 4, 5760, 60], 'label': '9000.o.150.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '150.e1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997796
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '30.g1.a1', '50.b1.a1', '75.a1.a1'], 'contains': ['300.k1.a1', '450.e1.a1', '750.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6161, -1, 863, -1, 7211, -1, 6602, -1], 'generators': [5733, 102, 24, 4], 'label': '9000.o.150.f1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.f1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997797
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '30.h1.a1', '30.i1.a1', '30.i1.b1', '75.b1.a1'], 'contains': ['300.l1.a1', '450.f1.a1', '750.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9365, -1, 2125, -1, 8244, -1, 7454, -1], 'generators': [5733, 102, 384, 4], 'label': '9000.o.150.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '150.g1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997798
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '30.h1.b1', '30.i1.b1', '30.i1.c1', '75.b1.b1'], 'contains': ['300.l1.b1', '450.f1.b1', '750.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9365, -1, 1708, -1, 8244, -1, 7165, -1], 'generators': [5733, 102, 744, 4], 'label': '9000.o.150.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '150.g1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.g1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997799
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '30.h1.b1', '30.i1.a1', '30.i1.d1', '75.b1.c1'], 'contains': ['300.l1.c1', '450.f1.c1', '750.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9365, -1, 1335, -1, 8244, -1, 7261, -1], 'generators': [5733, 102, 1104, 4], 'label': '9000.o.150.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '150.g1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.g1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997800
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '30.h1.a1', '30.i1.c1', '30.i1.d1', '75.b1.d1'], 'contains': ['300.l1.d1', '450.f1.d1', '750.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9365, -1, 1439, -1, 8244, -1, 7358, -1], 'generators': [5733, 102, 1464, 4], 'label': '9000.o.150.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '150.g1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.g1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997801
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.f1.a1', '30.h1.a1', '30.h1.b1', '30.j1.a1', '75.c1.a1'], 'contains': ['300.m1.a1', '450.g1.a1', '750.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7369, -1, 652, -1, 7750, -1, 6988, -1], 'generators': [5733, 102, 360, 4], 'label': '9000.o.150.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '150.h1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.h1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997802
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.a1', '30.i1.a1', '30.i1.b1', '30.i1.c1', '30.i1.d1', '30.j1.a1', '75.e1.a1'], 'contains': ['300.n1.a1', '450.h1.a1', '750.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8841, -1, 2043, -1, 7351, -1, 6891, -1], 'generators': [5733, 102, 3960, 4], 'label': '9000.o.150.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '150.i1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.i1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997803
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.a1', '30.h1.a1', '30.h1.b1', '30.i1.a1', '30.i1.c1'], 'contains': ['300.o1.a1', '450.i1.a1', '750.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [9122, -1, 1048, -1, 7610, -1, 6795, -1], 'generators': [5733, 102, 2184, 4], 'label': '9000.o.150.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.j1.a1', 'old_label': '150.j1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.j1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997804
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.g1.a1', '30.h1.a1', '30.h1.b1', '30.i1.b1', '30.i1.d1'], 'contains': ['300.o1.b1', '450.i1.b1', '750.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [9122, -1, 1136, -1, 7610, -1, 6698, -1], 'generators': [5733, 102, 2544, 4], 'label': '9000.o.150.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.j1.b1', 'old_label': '150.j1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.j1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997805
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': ['1125.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '40.a1.a1', '200.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1237, 2837, 9134, 7057, 670, 3462, 234, 3477], 'generators': [4, 24, 7560, 1200, 1800], 'label': '9000.o.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '3000.bf', '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': '600.151'}
  • id: 68997806
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.k1.a1', '30.l1.a1', '50.c1.a1', '75.a1.a1'], 'contains': ['300.k1.a1', '450.j1.a1', '750.d1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7540, -1, 3922, -1, 9116, -1, 8213, -1], 'generators': [3, 6, 24, 4], 'label': '9000.o.150.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '150.k1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.k1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997807
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.k1.a1', '30.m1.a1', '75.b1.a1'], 'contains': ['300.l1.a1', '450.k1.a1', '750.d1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9974, -1, 3094, -1, 9939, -1, 9877, -1], 'generators': [3, 6, 3264, 4], 'label': '9000.o.150.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '150.l1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.l1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997808
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.k1.a1', '30.m1.b1', '75.b1.b1'], 'contains': ['300.l1.b1', '450.k1.b1', '750.d1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9974, -1, 3276, -1, 9939, -1, 9393, -1], 'generators': [3, 6, 4704, 4], 'label': '9000.o.150.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '150.l1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.l1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997809
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.k1.a1', '30.m1.d1', '75.b1.c1'], 'contains': ['300.l1.c1', '450.k1.c1', '750.d1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9974, -1, 3347, -1, 9939, -1, 9554, -1], 'generators': [3, 6, 6144, 4], 'label': '9000.o.150.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '150.l1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.l1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997810
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.k1.a1', '30.m1.c1', '75.b1.d1'], 'contains': ['300.l1.d1', '450.k1.d1', '750.d1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9974, -1, 3165, -1, 9939, -1, 9781, -1], 'generators': [3, 6, 7584, 4], 'label': '9000.o.150.l1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '150.l1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.l1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997811
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.k1.a1', '30.n1.a1', '75.c1.a1'], 'contains': ['300.m1.a1', '450.l1.a1', '750.d1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8412, -1, 2983, -1, 9586, -1, 9038, -1], 'generators': [3, 6, 7560, 4], 'label': '9000.o.150.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '150.m1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.m1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997812
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.l1.a1', '30.m1.a1', '30.m1.b1', '30.m1.c1', '30.m1.d1', '30.n1.a1', '75.e1.a1'], 'contains': ['300.n1.a1', '450.m1.a1', '750.d1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9610, -1, 4380, -1, 9446, -1, 8941, -1], 'generators': [3, 6, 2160, 4], 'label': '9000.o.150.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '150.n1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.n1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997813
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '50.b1.a1', '75.d1.a1'], 'contains': ['300.p1.a1', '450.e1.a1', '750.e1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5391, -1, 142, -1, 2613, -1, 1793, -1], 'generators': [5733, 102, 24, 1200], 'label': '9000.o.150.o1.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.o1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.o1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997814
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '50.c1.a1', '75.d1.a1'], 'contains': ['300.p1.a1', '450.j1.a1', '750.f1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6851, -1, 2783, -1, 3045, -1, 2117, -1], 'generators': [3, 1200, 24, 6], 'label': '9000.o.150.p1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '150.p1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.p1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 68997815
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '150.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '50.b1.a1'], 'contains': ['300.q1.a1', '450.e1.a1', '750.g1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [5953, -1, 31, -1, 2262, -1, 1552, -1], 'generators': [5733, 102, 24, 1204], 'label': '9000.o.150.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '150.q1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '150.q1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997816
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '45.a1.a1', '45.b1.a1', '45.c1.a1', '45.c1.b1', '45.c1.c1', '45.c1.d1', '45.d1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7748, -1, 2374, -1, 8150, -1, 8089, -1], 'generators': [1203, 1800, 6, 24, 60, 360], 'label': '9000.o.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.168'}
  • id: 68997817
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.b1.a1', '90.a1.a1'], 'contains': ['360.b1.a1', '900.a1.a1', '900.b1.a1', '900.b1.b1', '900.b1.c1', '900.b1.d1', '900.c1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [841, -1, 7580, -1, 5021, -1, 4538, -1], 'generators': [60, 360, 24], 'label': '9000.o.180.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '180.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997818
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.c1.a1', '90.b1.a1'], 'contains': ['360.c1.a1', '900.a1.a1', '900.d1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1679, -1, 8482, -1, 4290, -1, 1768, -1], 'generators': [60, 5760, 24], 'label': '9000.o.180.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '180.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997819
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.d1.a1', '90.c1.a1'], 'contains': ['360.e1.a1', '900.b1.a1', '900.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3634, -1, 9275, -1, 5177, -1, 2907, -1], 'generators': [60, 5760, 3624], 'label': '9000.o.180.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '180.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997820
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.d1.b1', '90.c1.b1'], 'contains': ['360.e1.b1', '900.b1.b1', '900.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3634, -1, 9897, -1, 5177, -1, 2613, -1], 'generators': [60, 5760, 7224], 'label': '9000.o.180.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '180.c1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997821
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.d1.c1', '90.c1.c1'], 'contains': ['360.e1.c1', '900.b1.d1', '900.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3634, -1, 9826, -1, 5177, -1, 2809, -1], 'generators': [60, 5760, 5424], 'label': '9000.o.180.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '180.c1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.c1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997822
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.d1.d1', '90.c1.d1'], 'contains': ['360.e1.d1', '900.b1.c1', '900.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3634, -1, 8666, -1, 5177, -1, 2711, -1], 'generators': [60, 5760, 1824], 'label': '9000.o.180.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '180.c1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.c1.d1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997823
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '60.a1.a1', '60.e1.a1', '90.d1.a1'], 'contains': ['360.a1.a1', '900.c1.a1', '900.d1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1396, -1, 9969, -1, 3684, -1, 1670, -1], 'generators': [60, 5760, 1800], 'label': '9000.o.180.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '180.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.d1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997824
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.f1.a1', '90.b1.a1'], 'contains': ['360.c1.a1', '900.e1.a1', '900.f1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3014, -1, 7778, -1, 3040, -1, 2203, -1], 'generators': [114, 24, 5760], 'label': '9000.o.180.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.e1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997825
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.g1.a1', '90.c1.a1'], 'contains': ['360.e1.a1', '900.e1.a1', '900.g1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5309, -1, 8594, -1, 3827, -1, 3944, -1], 'generators': [114, 384, 5760], 'label': '9000.o.180.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '180.f1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997826
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.g1.b1', '90.c1.b1'], 'contains': ['360.e1.b1', '900.e1.a1', '900.g1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5309, -1, 9010, -1, 3827, -1, 3301, -1], 'generators': [114, 744, 5760], 'label': '9000.o.180.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '180.f1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997827
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.a1.a1', '6.e1.a1', '10.a1.a1', '50.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1888, 3767, 6151, 5731, 1720, 3586, 1238, 3904], 'generators': [6, 7560, 4, 1200, 60, 1800, 24], 'label': '9000.o.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '3000.bf', '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': '3000.bf'}
  • id: 68997828
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '30.d1.a1', '30.e1.a1', '250.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1610, -1, 6142, -1, 1641, -1, 1091, -1], 'generators': [6, 1800, 4, 1200, 60, 7560], 'label': '9000.o.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': '3000.bf', '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': '600.151'}
  • id: 68997829
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.g1.c1', '90.c1.c1'], 'contains': ['360.e1.c1', '900.e1.a1', '900.g1.d1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5309, -1, 8898, -1, 3827, -1, 3730, -1], 'generators': [114, 1464, 5760], 'label': '9000.o.180.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '180.f1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.c1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997830
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.g1.d1', '90.c1.d1'], 'contains': ['360.e1.d1', '900.e1.a1', '900.g1.c1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5309, -1, 8110, -1, 3827, -1, 3399, -1], 'generators': [114, 1104, 5760], 'label': '9000.o.180.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '180.f1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.f1.d1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997831
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.h1.a1', '60.i1.a1', '90.d1.a1'], 'contains': ['360.a1.a1', '900.e1.a1', '900.h1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3148, -1, 9123, -1, 2897, -1, 2105, -1], 'generators': [114, 360, 1800], 'label': '9000.o.180.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '180.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.g1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997832
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '60.j1.a1', '90.a1.a1'], 'contains': ['360.b1.a1', '900.f1.a1', '900.g1.a1', '900.g1.b1', '900.g1.c1', '900.g1.d1', '900.h1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2457, -1, 6848, -1, 3395, -1, 5182, -1], 'generators': [114, 360, 24], 'label': '9000.o.180.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '180.h1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.h1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997833
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.k1.a1', '90.a1.a1', '90.e1.a1', '90.j1.a1'], 'contains': ['360.b1.a1', '900.i1.a1', '900.j1.a1', '900.j1.b1', '900.j1.c1', '900.j1.d1', '900.k1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4606, -1, 3876, -1, 7006, -1, 7252, -1], 'generators': [6, 360, 24], 'label': '9000.o.180.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '180.i1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.i1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997834
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.l1.a1', '90.b1.a1', '90.f1.a1', '90.k1.a1'], 'contains': ['360.c1.a1', '900.i1.a1', '900.l1.a1', '900.m1.a1', '900.m1.b1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5123, -1, 4669, -1, 6624, -1, 6348, -1], 'generators': [6, 3960, 24], 'label': '9000.o.180.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '180.j1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.j1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997835
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.m1.a1', '90.g1.a1'], 'contains': ['360.d1.a1', '900.j1.a1', '900.j1.d1', '900.k1.a1', '900.m1.a1', '900.m1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5865, -1, 3747, -1, 7102, -1, 7135, -1], 'generators': [6, 360, 1824], 'label': '9000.o.180.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.h1.a1', 'old_label': '180.k1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.k1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997836
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.m1.b1', '90.g1.b1'], 'contains': ['360.d1.b1', '900.j1.b1', '900.j1.c1', '900.k1.a1', '900.m1.a1', '900.m1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [5865, -1, 3316, -1, 7102, -1, 6938, -1], 'generators': [6, 360, 3624], 'label': '9000.o.180.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.h1.b1', 'old_label': '180.k1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.k1.b1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68997837
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.n1.a1', '90.c1.a1', '90.h1.a1', '90.l1.a1'], 'contains': ['360.e1.a1', '900.j1.a1', '900.j1.c1', '900.l1.a1', '900.m1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7931, -1, 4415, -1, 7272, -1, 7069, -1], 'generators': [6, 3960, 7224], 'label': '9000.o.180.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '180.l1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997858
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.d1.d1', '150.b1.c1'], 'contains': ['600.b1.c1', '900.b1.c1', '1500.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3737, -1, 7799, -1, 5464, -1, 4151, -1], 'generators': [60, 1104, 4], 'label': '9000.o.300.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '300.b1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.b1.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997838
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.n1.b1', '90.c1.b1', '90.h1.b1', '90.l1.b1'], 'contains': ['360.e1.b1', '900.j1.a1', '900.j1.b1', '900.l1.a1', '900.m1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7931, -1, 5036, -1, 7272, -1, 6806, -1], 'generators': [6, 3960, 5424], 'label': '9000.o.180.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '180.l1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997839
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '30.j1.a1', '30.o1.a1', '30.q1.a1', '250.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5803, -1, 1156, -1, 2440, -1, 1601, -1], 'generators': [5733, 1800, 1200, 102, 4, 360], 'label': '9000.o.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': '3000.bf', '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': '600.151'}
  • id: 68997840
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.n1.c1', '90.c1.c1', '90.h1.c1', '90.l1.c1'], 'contains': ['360.e1.c1', '900.j1.b1', '900.j1.d1', '900.l1.a1', '900.m1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7931, -1, 4347, -1, 7272, -1, 7004, -1], 'generators': [6, 3960, 1824], 'label': '9000.o.180.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '180.l1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997841
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.n1.d1', '90.c1.d1', '90.h1.d1', '90.l1.d1'], 'contains': ['360.e1.d1', '900.j1.c1', '900.j1.d1', '900.l1.a1', '900.m1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7931, -1, 4907, -1, 7272, -1, 6872, -1], 'generators': [6, 3960, 3624], 'label': '9000.o.180.l1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '180.l1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.l1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997842
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '180.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '60.o1.a1', '60.p1.a1', '60.q1.a1', '90.d1.a1', '90.i1.a1', '90.m1.a1'], 'contains': ['360.a1.a1', '900.k1.a1', '900.l1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [4737, -1, 5104, -1, 6149, -1, 5313, -1], 'generators': [6, 1800, 360], 'label': '9000.o.180.m1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '180.m1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.m1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68997843
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '100.a1.a1', '100.b1.a1', '100.c1.a1'], 'contains': ['600.a1.a1', '600.f1.a1', '600.g1.a1', '1000.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [348, -1, 8216, -1, 982, -1, 590, -1], 'generators': [4, 24, 1200], 'label': '9000.o.200.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '200.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997844
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '225.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '45.b1.a1', '75.a1.a1', '75.d1.a1'], 'contains': ['450.a1.a1', '450.e1.a1', '450.j1.a1', '1125.a1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6713, -1, 1629, -1, 8384, -1, 8116, -1], 'generators': [1203, 6, 24, 60], 'label': '9000.o.225.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '225.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997845
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '225.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '45.c1.a1', '75.b1.a1'], 'contains': ['450.b1.a1', '450.f1.a1', '450.k1.a1', '1125.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9731, -1, 2513, -1, 8975, -1, 9231, -1], 'generators': [1203, 6, 384, 60], 'label': '9000.o.225.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '225.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997846
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '225.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '45.c1.b1', '75.b1.b1'], 'contains': ['450.b1.b1', '450.f1.b1', '450.k1.b1', '1125.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9731, -1, 2824, -1, 8975, -1, 8749, -1], 'generators': [1203, 6, 744, 60], 'label': '9000.o.225.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '225.b1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997847
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '225.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '45.c1.d1', '75.b1.c1'], 'contains': ['450.b1.c1', '450.f1.c1', '450.k1.c1', '1125.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9731, -1, 1920, -1, 8975, -1, 8845, -1], 'generators': [1203, 6, 1104, 60], 'label': '9000.o.225.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '225.b1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.b1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997848
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '225.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '45.c1.c1', '75.b1.d1'], 'contains': ['450.b1.d1', '450.f1.d1', '450.k1.d1', '1125.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9731, -1, 2090, -1, 8975, -1, 9134, -1], 'generators': [1203, 6, 1464, 60], 'label': '9000.o.225.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '225.b1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.b1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997849
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '225.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.a1.a1', '45.d1.a1', '75.c1.a1'], 'contains': ['450.c1.a1', '450.g1.a1', '450.l1.a1', '1125.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8105, -1, 1371, -1, 8835, -1, 8652, -1], 'generators': [1203, 6, 360, 60], 'label': '9000.o.225.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '225.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997850
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '10.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '30.n1.a1', '30.p1.a1', '250.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7459, -1, 4310, -1, 3401, -1, 2233, -1], 'generators': [3, 1800, 6, 1200, 4, 5760], 'label': '9000.o.10.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '10.c1.a1', 'projective_image': '3000.bf', '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': '600.151'}
  • id: 68997851
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '225.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['45.b1.a1', '45.c1.a1', '45.c1.b1', '45.c1.c1', '45.c1.d1', '45.d1.a1', '75.e1.a1'], 'contains': ['450.d1.a1', '450.h1.a1', '450.m1.a1', '1125.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9210, -1, 2421, -1, 8694, -1, 8439, -1], 'generators': [1203, 6, 5760, 60], 'label': '9000.o.225.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '225.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '225.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997852
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '250.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '750.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '50.a1.a1', '125.a1.a1'], 'contains': ['500.a1.a1', '500.b1.a1', '500.c1.a1', '750.a1.a1', '750.b1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [1161, -1, 5666, -1, 1379, -1, 1191, -1], 'generators': [6, 60, 4, 1200], 'label': '9000.o.250.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '250.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '250.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997853
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '250.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '250.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '50.b1.a1', '125.a1.a1'], 'contains': ['500.c1.a1', '750.c1.a1', '750.e1.a1', '750.g1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [5789, -1, 188, -1, 2417, -1, 1687, -1], 'generators': [5733, 4, 1200, 102], 'label': '9000.o.250.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '250.b1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '250.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68997854
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '250.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '750.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.c1.a1', '50.c1.a1', '125.a1.a1'], 'contains': ['500.c1.a1', '750.d1.a1', '750.f1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [7269, -1, 3434, -1, 2911, -1, 2025, -1], 'generators': [3, 4, 6, 1200], 'label': '9000.o.250.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '250.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '250.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997855
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.c1.a1', '100.a1.a1', '150.a1.a1'], 'contains': ['600.a1.a1', '900.a1.a1', '1500.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [876, -1, 8032, -1, 4172, -1, 1965, -1], 'generators': [60, 24, 4], 'label': '9000.o.300.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '300.a1.a1', 'projective_image': '3000.bf', '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': '4.1'}
  • id: 68997856
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.d1.a1', '150.b1.a1'], 'contains': ['600.b1.a1', '900.b1.a1', '1500.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3737, -1, 7704, -1, 5464, -1, 4628, -1], 'generators': [60, 384, 4], 'label': '9000.o.300.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '300.b1.a1', 'projective_image': '3000.bf', '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': '4.1'}
  • id: 68997857
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.d1.b1', '150.b1.b1'], 'contains': ['600.b1.b1', '900.b1.b1', '1500.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3737, -1, 7552, -1, 5464, -1, 4088, -1], 'generators': [60, 744, 4], 'label': '9000.o.300.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '300.b1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997859
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.d1.c1', '150.b1.d1'], 'contains': ['600.b1.d1', '900.b1.d1', '1500.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3737, -1, 7906, -1, 5464, -1, 4331, -1], 'generators': [60, 1464, 4], 'label': '9000.o.300.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '300.b1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.b1.d1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997860
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '60.e1.a1', '150.c1.a1'], 'contains': ['600.c1.a1', '900.c1.a1', '1500.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1222, -1, 7502, -1, 4890, -1, 4025, -1], 'generators': [60, 360, 4], 'label': '9000.o.300.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '300.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997861
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': ['750.d1.a1', '750.c1.a1', '750.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '36.b1.a1', '60.a1.a1', '300.d1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [592, 1723, 8883, 8215, 1230, 1989, 512, 1998], 'generators': [60, 1200, 5760, 24, 1800], 'label': '9000.o.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.b1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '9000.o', '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': '600.151'}
  • id: 68997862
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '100.a1.a1', '150.d1.a1'], 'contains': ['600.f1.a1', '900.a1.a1', '1500.b1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [177, -1, 8498, -1, 1609, -1, 793, -1], 'generators': [60, 1200, 24], 'label': '9000.o.300.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '300.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 68997863
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '60.d1.a1', '60.d1.b1', '60.d1.c1', '60.d1.d1', '60.e1.a1', '150.e1.a1'], 'contains': ['600.d1.a1', '900.d1.a1', '1500.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2058, -1, 9360, -1, 4602, -1, 2515, -1], 'generators': [60, 5760, 4], 'label': '9000.o.300.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '300.e1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997864
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '60.g1.a1', '60.g1.b1', '60.g1.c1', '60.g1.d1', '60.h1.a1', '150.e1.a1'], 'contains': ['600.d1.a1', '900.e1.a1', '1500.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4481, -1, 8936, -1, 3157, -1, 3104, -1], 'generators': [114, 5760, 4], 'label': '9000.o.300.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '300.f1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997865
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.f1.a1', '60.j1.a1', '100.b1.a1', '150.a1.a1'], 'contains': ['600.a1.a1', '900.f1.a1', '1500.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1814, -1, 7353, -1, 2754, -1, 2417, -1], 'generators': [114, 24, 4], 'label': '9000.o.300.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '300.g1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997866
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.g1.a1', '60.j1.a1', '150.b1.a1'], 'contains': ['600.b1.a1', '900.g1.a1', '1500.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4932, -1, 6768, -1, 3969, -1, 5100, -1], 'generators': [114, 384, 4], 'label': '9000.o.300.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '300.h1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.h1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997867
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.g1.b1', '60.j1.a1', '150.b1.b1'], 'contains': ['600.b1.b1', '900.g1.b1', '1500.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4932, -1, 6675, -1, 3969, -1, 4806, -1], 'generators': [114, 744, 4], 'label': '9000.o.300.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '300.h1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.h1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997868
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.g1.d1', '60.j1.a1', '150.b1.c1'], 'contains': ['600.b1.c1', '900.g1.c1', '1500.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4932, -1, 6839, -1, 3969, -1, 4904, -1], 'generators': [114, 1104, 4], 'label': '9000.o.300.h1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '300.h1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.h1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997869
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.g1.c1', '60.j1.a1', '150.b1.d1'], 'contains': ['600.b1.d1', '900.g1.d1', '1500.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4932, -1, 6952, -1, 3969, -1, 5002, -1], 'generators': [114, 1464, 4], 'label': '9000.o.300.h1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '300.h1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.h1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997870
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.h1.a1', '60.j1.a1', '150.c1.a1'], 'contains': ['600.c1.a1', '900.h1.a1', '1500.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3277, -1, 6463, -1, 3275, -1, 4708, -1], 'generators': [114, 360, 4], 'label': '9000.o.300.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '300.i1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.i1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997871
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '100.b1.a1', '150.d1.a1'], 'contains': ['600.f1.a1', '900.f1.a1', '1500.d1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [600, -1, 8325, -1, 1153, -1, 997, -1], 'generators': [114, 24, 1200], 'label': '9000.o.300.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '300.j1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.j1.a1', 'subgroup_fusion': None, 'weyl_group': '120.36'}
  • id: 68997872
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': ['750.d1.a1', '750.c1.a1', '750.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.b1.a1', '36.c1.a1', '60.i1.a1', '300.j1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [977, 4381, 8325, 5412, 841, 4663, 782, 4684], 'generators': [114, 24, 3960, 1200, 1800], 'label': '9000.o.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': '4.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3000.bf'}
  • id: 68997873
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '60.l1.a1', '100.c1.a1', '150.a1.a1', '150.f1.a1', '150.k1.a1'], 'contains': ['600.a1.a1', '900.i1.a1', '1500.e1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [4223, -1, 4757, -1, 6361, -1, 5747, -1], 'generators': [6, 24, 4], 'label': '9000.o.300.k1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '300.k1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.k1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997874
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '60.m1.a1', '60.n1.a1', '60.n1.b1', '150.b1.a1', '150.g1.a1', '150.l1.a1'], 'contains': ['600.b1.a1', '900.j1.a1', '1500.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8108, -1, 4246, -1, 7392, -1, 6724, -1], 'generators': [6, 384, 4], 'label': '9000.o.300.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '300.l1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.l1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997875
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '60.m1.b1', '60.n1.b1', '60.n1.c1', '150.b1.b1', '150.g1.b1', '150.l1.b1'], 'contains': ['600.b1.b1', '900.j1.b1', '1500.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8108, -1, 4098, -1, 7392, -1, 6430, -1], 'generators': [6, 744, 4], 'label': '9000.o.300.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '300.l1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.l1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997876
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '60.m1.b1', '60.n1.a1', '60.n1.d1', '150.b1.c1', '150.g1.c1', '150.l1.c1'], 'contains': ['600.b1.c1', '900.j1.c1', '1500.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8108, -1, 4173, -1, 7392, -1, 6528, -1], 'generators': [6, 1104, 4], 'label': '9000.o.300.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '300.l1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.l1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997877
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '60.m1.a1', '60.n1.c1', '60.n1.d1', '150.b1.d1', '150.g1.d1', '150.l1.d1'], 'contains': ['600.b1.d1', '900.j1.d1', '1500.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8108, -1, 4393, -1, 7392, -1, 6626, -1], 'generators': [6, 1464, 4], 'label': '9000.o.300.l1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '300.l1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.l1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997878
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.k1.a1', '60.m1.a1', '60.m1.b1', '60.o1.a1', '150.c1.a1', '150.h1.a1', '150.m1.a1'], 'contains': ['600.c1.a1', '900.k1.a1', '1500.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5252, -1, 3560, -1, 6744, -1, 6266, -1], 'generators': [6, 360, 4], 'label': '9000.o.300.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '300.m1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.m1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997879
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.l1.a1', '60.n1.a1', '60.n1.b1', '60.n1.c1', '60.n1.d1', '60.o1.a1', '150.e1.a1', '150.i1.a1', '150.n1.a1'], 'contains': ['600.d1.a1', '900.l1.a1', '1500.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6603, -1, 6071, -1, 6504, -1, 5972, -1], 'generators': [6, 3960, 4], 'label': '9000.o.300.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '300.n1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.n1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997880
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.l1.a1', '60.m1.a1', '60.m1.b1', '60.n1.a1', '60.n1.c1', '150.j1.a1'], 'contains': ['600.e1.a1', '900.m1.a1', '1500.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [7678, -1, 5076, -1, 6886, -1, 6168, -1], 'generators': [6, 2184, 4], 'label': '9000.o.300.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.j1.a1', 'old_label': '300.o1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.o1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997881
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.l1.a1', '60.m1.a1', '60.m1.b1', '60.n1.b1', '60.n1.d1', '150.j1.b1'], 'contains': ['600.e1.b1', '900.m1.b1', '1500.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [7678, -1, 4637, -1, 6886, -1, 6070, -1], 'generators': [6, 2544, 4], 'label': '9000.o.300.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.j1.b1', 'old_label': '300.o1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.o1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997882
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '100.c1.a1', '150.d1.a1', '150.o1.a1', '150.p1.a1'], 'contains': ['600.f1.a1', '900.i1.a1', '1500.f1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [2601, -1, 5269, -1, 2152, -1, 1380, -1], 'generators': [6, 24, 1200], 'label': '9000.o.300.p1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '300.p1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.p1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997883
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.e1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '60.k1.a1', '60.l1.a1', '60.m1.a1', '60.m1.b1', '60.n1.a1', '60.n1.b1', '60.n1.c1', '60.n1.d1', '60.o1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5382, 6715, 5049, 3195, 6443, 6736, 5855, 6707], 'generators': [6, 24, 360, 4, 1800], 'label': '9000.o.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.b1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3000.bf'}
  • id: 68997884
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '300.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '100.c1.a1', '150.q1.a1'], 'contains': ['600.g1.a1', '900.i1.a1', '1500.g1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [2920, -1, 1201, -1, 1867, -1, 1184, -1], 'generators': [6, 24, 1204], 'label': '9000.o.300.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '300.q1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.q1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997885
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '360.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': ['25.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.a1.a1', '120.b1.a1', '120.g1.a1', '180.d1.a1', '180.g1.a1', '180.m1.a1'], 'contains': ['1800.c1.a1', '1800.d1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2086, 3171, 9439, 6301, 3650, 4121, 2026, 4080], 'generators': [360, 1800], 'label': '9000.o.360.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '360.a1.a1', 'normal_contained_in': ['72.a1.a1', '120.a1.a1', '120.b1.a1'], 'normal_contains': ['9000.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '360.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': '24.5', 'quotient_action_kernel': '15.1', 'quotient_action_kernel_order': 15, 'quotient_fusion': None, 'short_label': '360.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 68997886
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '360.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.c1.a1', '180.a1.a1', '180.h1.a1', '180.i1.a1'], 'contains': ['1800.a1.a1', '1800.b1.a1', '1800.b1.b1', '1800.b1.c1', '1800.b1.d1', '1800.c1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1686, -1, 6993, -1, 4848, -1, 4569, -1], 'generators': [24, 360], 'label': '9000.o.360.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '360.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997887
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '360.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.d1.a1', '180.b1.a1', '180.e1.a1', '180.j1.a1'], 'contains': ['1800.a1.a1', '1800.d1.a1', '1800.e1.a1', '1800.e1.b1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3058, -1, 8312, -1, 4429, -1, 2449, -1], 'generators': [24, 3960], 'label': '9000.o.360.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '360.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997888
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.e1.a1', '180.k1.a1'], 'contains': ['1800.b1.a1', '1800.b1.d1', '1800.c1.a1', '1800.e1.a1', '1800.e1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3973, -1, 6440, -1, 5700, -1, 4270, -1], 'generators': [1824, 360], 'label': '9000.o.360.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '360.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997889
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '360.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.e1.b1', '180.k1.b1'], 'contains': ['1800.b1.b1', '1800.b1.c1', '1800.c1.a1', '1800.e1.a1', '1800.e1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3973, -1, 6365, -1, 5700, -1, 3603, -1], 'generators': [3624, 360], 'label': '9000.o.360.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '360.d1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.d1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997890
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.f1.a1', '180.c1.a1', '180.f1.a1', '180.l1.a1'], 'contains': ['1800.b1.a1', '1800.b1.c1', '1800.d1.a1', '1800.e1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5108, -1, 8970, -1, 5034, -1, 3720, -1], 'generators': [7224, 3960], 'label': '9000.o.360.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '360.e1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997891
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.f1.b1', '180.c1.b1', '180.f1.b1', '180.l1.b1'], 'contains': ['1800.b1.a1', '1800.b1.b1', '1800.d1.a1', '1800.e1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5108, -1, 9661, -1, 5034, -1, 3341, -1], 'generators': [5424, 3960], 'label': '9000.o.360.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '360.e1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997892
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.f1.c1', '180.c1.c1', '180.f1.c1', '180.l1.c1'], 'contains': ['1800.b1.b1', '1800.b1.d1', '1800.d1.a1', '1800.e1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5108, -1, 9720, -1, 5034, -1, 3661, -1], 'generators': [1824, 3960], 'label': '9000.o.360.e1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '360.e1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.c1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997893
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '360.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '120.f1.d1', '180.c1.d1', '180.f1.d1', '180.l1.d1'], 'contains': ['1800.b1.c1', '1800.b1.d1', '1800.d1.a1', '1800.e1.b1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5108, -1, 8727, -1, 5034, -1, 3399, -1], 'generators': [3624, 3960], 'label': '9000.o.360.e1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '360.e1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '360.e1.d1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997894
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.c1.a1', '6.d1.a1'], 'contains': ['24.b1.a1', '36.a1.a1', '60.p1.a1', '300.p1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2122, 5391, 4801, 4463, 2158, 5586, 1419, 5596], 'generators': [6, 24, 360, 1200, 1800], 'label': '9000.o.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1', '6.c1.a1', '6.d1.a1'], 'normal_contains': ['24.b1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '3000.bf'}
  • id: 68997895
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '375.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '375.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['75.a1.a1', '75.b1.a1', '75.b1.b1', '75.b1.c1', '75.b1.d1', '75.c1.a1', '75.e1.a1', '125.a1.a1'], 'contains': ['750.a1.a1', '750.c1.a1', '750.d1.a1', '1125.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': [9195, -1, 2340, -1, 8539, -1, 8546, -1], 'generators': [1203, 60, 4, 6], 'label': '9000.o.375.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '375.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '375.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997896
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '375.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '750.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.e1.a1', '75.d1.a1', '125.a1.a1'], 'contains': ['750.b1.a1', '750.e1.a1', '750.f1.a1', '1125.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [6395, -1, 327, -1, 2753, -1, 1890, -1], 'generators': [3, 60, 6, 1200], 'label': '9000.o.375.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '375.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '375.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997897
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.b1.a1', '150.a1.a1', '150.d1.a1', '225.a1.a1'], 'contains': ['900.a1.a1', '900.f1.a1', '900.i1.a1', '2250.a1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3389, -1, 5313, -1, 5557, -1, 5247, -1], 'generators': [6, 24, 60], 'label': '9000.o.450.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '450.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997898
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.c1.a1', '150.b1.a1', '225.b1.a1'], 'contains': ['900.b1.a1', '900.g1.a1', '900.j1.a1', '2250.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7700, -1, 5619, -1, 6244, -1, 5892, -1], 'generators': [6, 384, 60], 'label': '9000.o.450.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '450.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.b1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997899
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.c1.b1', '150.b1.b1', '225.b1.b1'], 'contains': ['900.b1.b1', '900.g1.b1', '900.j1.b1', '2250.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7700, -1, 5250, -1, 6244, -1, 5603, -1], 'generators': [6, 744, 60], 'label': '9000.o.450.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '450.b1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.b1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997900
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.c1.d1', '150.b1.c1', '225.b1.c1'], 'contains': ['900.b1.c1', '900.g1.c1', '900.j1.c1', '2250.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7700, -1, 5399, -1, 6244, -1, 5666, -1], 'generators': [6, 1104, 60], 'label': '9000.o.450.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '450.b1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.b1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997901
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.c1.c1', '150.b1.d1', '225.b1.d1'], 'contains': ['900.b1.d1', '900.g1.d1', '900.j1.d1', '2250.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7700, -1, 5552, -1, 6244, -1, 5828, -1], 'generators': [6, 1464, 60], 'label': '9000.o.450.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '450.b1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.b1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997902
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.a1.a1', '90.d1.a1', '150.c1.a1', '225.c1.a1'], 'contains': ['900.c1.a1', '900.h1.a1', '900.k1.a1', '2250.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4111, -1, 5505, -1, 6054, -1, 5539, -1], 'generators': [6, 360, 60], 'label': '9000.o.450.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '450.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.c1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997903
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.b1.a1', '90.c1.a1', '90.c1.b1', '90.c1.c1', '90.c1.d1', '90.d1.a1', '150.e1.a1', '225.d1.a1'], 'contains': ['900.d1.a1', '900.e1.a1', '900.l1.a1', '2250.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5561, -1, 6184, -1, 5792, -1, 5377, -1], 'generators': [6, 5760, 60], 'label': '9000.o.450.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '450.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997904
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.a1', '90.f1.a1', '150.f1.a1', '150.o1.a1', '150.q1.a1', '225.a1.a1'], 'contains': ['900.i1.a1', '2250.b1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6395, -1, 797, -1, 7187, -1, 7193, -1], 'generators': [5733, 24, 102], 'label': '9000.o.450.e1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '450.e1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.e1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997905
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '36.b1.a1', '60.b1.a1', '60.c1.a1', '60.d1.a1', '60.d1.b1', '60.d1.c1', '60.d1.d1', '60.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1912, -1, 8995, -1, 4504, -1, 2907, -1], 'generators': [60, 24, 1800, 4, 5760], 'label': '9000.o.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.e1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68997906
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.a1', '90.g1.a1', '90.h1.a1', '90.h1.b1', '150.g1.a1', '225.b1.a1'], 'contains': ['900.j1.a1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9431, -1, 2027, -1, 7997, -1, 7819, -1], 'generators': [5733, 384, 102], 'label': '9000.o.450.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '450.f1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997907
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.a1', '90.g1.b1', '90.h1.b1', '90.h1.c1', '150.g1.b1', '225.b1.b1'], 'contains': ['900.j1.b1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9431, -1, 1759, -1, 7997, -1, 7664, -1], 'generators': [5733, 744, 102], 'label': '9000.o.450.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '450.f1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.f1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997908
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.a1', '90.g1.b1', '90.h1.a1', '90.h1.d1', '150.g1.c1', '225.b1.c1'], 'contains': ['900.j1.c1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9431, -1, 1397, -1, 7997, -1, 7716, -1], 'generators': [5733, 1104, 102], 'label': '9000.o.450.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '450.f1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.f1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997909
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.a1', '90.g1.a1', '90.h1.c1', '90.h1.d1', '150.g1.d1', '225.b1.d1'], 'contains': ['900.j1.d1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9431, -1, 1492, -1, 7997, -1, 7767, -1], 'generators': [5733, 1464, 102], 'label': '9000.o.450.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '450.f1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.f1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997910
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.e1.a1', '90.g1.a1', '90.g1.b1', '90.i1.a1', '150.h1.a1', '225.c1.a1'], 'contains': ['900.k1.a1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [6969, -1, 759, -1, 7750, -1, 7561, -1], 'generators': [5733, 360, 102], 'label': '9000.o.450.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '450.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997911
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.f1.a1', '90.h1.a1', '90.h1.b1', '90.h1.c1', '90.h1.d1', '90.i1.a1', '150.i1.a1', '225.d1.a1'], 'contains': ['900.l1.a1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8481, -1, 1855, -1, 7593, -1, 7613, -1], 'generators': [5733, 3960, 102], 'label': '9000.o.450.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '450.h1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.h1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997912
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.f1.a1', '90.g1.a1', '90.g1.b1', '90.h1.a1', '90.h1.c1', '150.j1.a1'], 'contains': ['900.m1.a1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [8590, -1, 906, -1, 7668, -1, 7510, -1], 'generators': [5733, 2184, 102], 'label': '9000.o.450.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.j1.a1', 'old_label': '450.i1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.i1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997913
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.f1.a1', '90.g1.a1', '90.g1.b1', '90.h1.b1', '90.h1.d1', '150.j1.b1'], 'contains': ['900.m1.b1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [8590, -1, 995, -1, 7668, -1, 7458, -1], 'generators': [5733, 2544, 102], 'label': '9000.o.450.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.j1.b1', 'old_label': '450.i1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.i1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997914
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.j1.a1', '90.k1.a1', '150.k1.a1', '150.p1.a1', '225.a1.a1'], 'contains': ['900.i1.a1', '2250.c1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7147, -1, 2702, -1, 9012, -1, 8213, -1], 'generators': [3, 24, 6], 'label': '9000.o.450.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.a1.a1', 'old_label': '450.j1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.j1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997915
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.j1.a1', '90.l1.a1', '150.l1.a1', '225.b1.a1'], 'contains': ['900.j1.a1', '2250.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9799, -1, 2582, -1, 9532, -1, 9465, -1], 'generators': [3, 3264, 6], 'label': '9000.o.450.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '450.k1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.k1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997916
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '36.c1.a1', '60.f1.a1', '60.g1.a1', '60.g1.b1', '60.g1.c1', '60.g1.d1', '60.h1.a1', '60.j1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3442, -1, 8485, -1, 3705, -1, 3511, -1], 'generators': [114, 1800, 24, 4, 360], 'label': '9000.o.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.f1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '200.47'}
  • id: 68997917
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.j1.a1', '90.l1.b1', '150.l1.b1', '225.b1.b1'], 'contains': ['900.j1.b1', '2250.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9799, -1, 2777, -1, 9532, -1, 9058, -1], 'generators': [3, 4704, 6], 'label': '9000.o.450.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '450.k1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.k1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997918
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.j1.a1', '90.l1.d1', '150.l1.c1', '225.b1.c1'], 'contains': ['900.j1.c1', '2250.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9799, -1, 3031, -1, 9532, -1, 9113, -1], 'generators': [3, 6144, 6], 'label': '9000.o.450.k1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '450.k1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.k1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997919
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.j1.a1', '90.l1.c1', '150.l1.d1', '225.b1.d1'], 'contains': ['900.j1.d1', '2250.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [9799, -1, 2459, -1, 9532, -1, 9401, -1], 'generators': [3, 7584, 6], 'label': '9000.o.450.k1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '450.k1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.k1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997920
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.j1.a1', '90.m1.a1', '150.m1.a1', '225.c1.a1'], 'contains': ['900.k1.a1', '2250.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7584, -1, 2622, -1, 9253, -1, 9005, -1], 'generators': [3, 7560, 6], 'label': '9000.o.450.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '450.l1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.l1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997921
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '450.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['90.k1.a1', '90.l1.a1', '90.l1.b1', '90.l1.c1', '90.l1.d1', '90.m1.a1', '150.n1.a1', '225.d1.a1'], 'contains': ['900.l1.a1', '2250.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [8915, -1, 3260, -1, 9179, -1, 8891, -1], 'generators': [3, 2160, 6], 'label': '9000.o.450.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '450.m1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '450.m1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997922
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '500.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '150.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '100.a1.a1', '250.a1.a1'], 'contains': ['1000.a1.a1', '1500.a1.a1', '1500.b1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [139, -1, 8876, -1, 1428, -1, 696, -1], 'generators': [60, 4, 1200], 'label': '9000.o.500.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '500.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '500.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997923
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '500.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '750.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '100.b1.a1', '250.a1.a1'], 'contains': ['1000.a1.a1', '1500.c1.a1', '1500.d1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [695, -1, 8486, -1, 709, -1, 917, -1], 'generators': [114, 4, 1200], 'label': '9000.o.500.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '500.b1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '500.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997924
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '500.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '250.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '100.c1.a1', '250.a1.a1', '250.b1.a1', '250.c1.a1'], 'contains': ['1000.a1.a1', '1500.e1.a1', '1500.f1.a1', '1500.g1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [2662, -1, 4968, -1, 2009, -1, 1282, -1], 'generators': [6, 4, 1200], 'label': '9000.o.500.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '500.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '500.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68997925
    {'ambient': '9000.o', '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': '4.a1.a1', 'complements': ['15.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.d1.a1', '200.a1.a1', '300.a1.a1', '300.g1.a1', '300.k1.a1'], 'contains': ['1800.a1.a1', '3000.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1120, 4250, 8164, 5269, 4249, 5645, 2509, 5611], 'generators': [4, 24], 'label': '9000.o.600.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '600.a1.a1', 'normal_contained_in': ['24.a1.a1'], 'normal_contains': ['1800.a1.a1', '3000.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '600.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': '4.1', 'quotient_action_kernel': '150.5', 'quotient_action_kernel_order': 150, 'quotient_fusion': None, 'short_label': '600.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997926
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.e1.a1', '120.f1.a1', '120.f1.b1', '300.b1.a1', '300.h1.a1', '300.l1.a1'], 'contains': ['1800.b1.a1', '3000.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4464, -1, 7264, -1, 5123, -1, 4457, -1], 'generators': [4, 384], 'label': '9000.o.600.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '600.b1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997927
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.g1.a1'], 'contains': ['24.c1.a1', '36.a1.a1', '60.q1.a1', '300.q1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2905, -1, 2895, -1, 1804, -1, 971, -1], 'generators': [6, 24, 360, 1204, 1800], 'label': '9000.o.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1500.119'}
  • id: 68997928
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.e1.b1', '120.f1.b1', '120.f1.c1', '300.b1.b1', '300.h1.b1', '300.l1.b1'], 'contains': ['1800.b1.b1', '3000.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4464, -1, 7218, -1, 5123, -1, 4021, -1], 'generators': [4, 744], 'label': '9000.o.600.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '600.b1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997929
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.e1.b1', '120.f1.a1', '120.f1.d1', '300.b1.c1', '300.h1.c1', '300.l1.c1'], 'contains': ['1800.b1.c1', '3000.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4464, -1, 7483, -1, 5123, -1, 4084, -1], 'generators': [4, 1104], 'label': '9000.o.600.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '600.b1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.b1.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997930
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '120.e1.a1', '120.f1.c1', '120.f1.d1', '300.b1.d1', '300.h1.d1', '300.l1.d1'], 'contains': ['1800.b1.d1', '3000.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4464, -1, 7622, -1, 5123, -1, 4331, -1], 'generators': [4, 1464], 'label': '9000.o.600.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '600.b1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.b1.d1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997931
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.c1.a1', '120.e1.a1', '120.e1.b1', '300.c1.a1', '300.i1.a1', '300.m1.a1'], 'contains': ['1800.c1.a1', '3000.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1926, -1, 6446, -1, 4759, -1, 3895, -1], 'generators': [4, 360], 'label': '9000.o.600.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '600.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997932
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '120.d1.a1', '120.f1.a1', '120.f1.b1', '120.f1.c1', '120.f1.d1', '300.e1.a1', '300.f1.a1', '300.n1.a1'], 'contains': ['1800.d1.a1', '3000.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3043, -1, 9301, -1, 4518, -1, 3194, -1], 'generators': [4, 3960], 'label': '9000.o.600.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '600.d1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997933
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '120.e1.a1', '120.e1.b1', '120.f1.a1', '120.f1.c1', '300.o1.a1'], 'contains': ['1800.e1.a1', '3000.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3790, -1, 7144, -1, 5325, -1, 3781, -1], 'generators': [4, 2184], 'label': '9000.o.600.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '600.e1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997934
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.d1.a1', '120.e1.a1', '120.e1.b1', '120.f1.b1', '120.f1.d1', '300.o1.b1'], 'contains': ['1800.e1.b1', '3000.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3790, -1, 7341, -1, 5325, -1, 3532, -1], 'generators': [4, 2544], 'label': '9000.o.600.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '600.e1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997935
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '200.a1.a1', '300.d1.a1', '300.j1.a1', '300.p1.a1'], 'contains': ['1800.a1.a1', '3000.b1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [311, -1, 8559, -1, 1540, -1, 968, -1], 'generators': [1200, 24], 'label': '9000.o.600.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '600.f1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 68997936
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '600.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '200.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '200.a1.a1', '300.q1.a1'], 'contains': ['1800.a1.a1', '3000.c1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [521, -1, 6114, -1, 1288, -1, 795, -1], 'generators': [1204, 24], 'label': '9000.o.600.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '600.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '600.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997937
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '750.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '375.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.a1.a1', '150.b1.a1', '150.b1.b1', '150.b1.c1', '150.b1.d1', '150.c1.a1', '150.e1.a1', '250.a1.a1', '375.a1.a1'], 'contains': ['1500.a1.a1', '1500.c1.a1', '1500.e1.a1', '2250.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': [4994, -1, 5787, -1, 5674, -1, 5458, -1], 'generators': [6, 60, 4], 'label': '9000.o.750.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '750.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997938
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': ['4500.a1.a1', '4500.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '6.b1.a1', '6.c1.a1', '6.g1.a1', '10.b1.a1', '50.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5846, 8118, 1109, 1792, 2538, 8187, 1646, 8525], 'generators': [5733, 360, 1200, 102, 4, 1800, 24], 'label': '9000.o.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '6.b1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '3000.bf', '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': '3000.bf'}
  • id: 68997939
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['30.a1.a1', '30.f1.a1', '30.k1.a1', '45.a1.a1', '75.a1.a1', '75.b1.a1', '75.b1.b1', '75.b1.c1', '75.b1.d1', '75.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7231, -1, 2497, -1, 8351, -1, 8467, -1], 'generators': [1203, 360, 4, 6, 60, 24], 'label': '9000.o.15.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '3000.bf', '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': '100.11'}
  • id: 68997940
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '750.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '750.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.e1.a1', '150.d1.a1', '250.a1.a1', '375.b1.a1'], 'contains': ['1500.b1.a1', '1500.d1.a1', '1500.f1.a1', '2250.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [1534, -1, 5419, -1, 1718, -1, 1109, -1], 'generators': [6, 60, 1200], 'label': '9000.o.750.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '750.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997941
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '750.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '125.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.f1.a1', '150.g1.a1', '150.g1.b1', '150.g1.c1', '150.g1.d1', '150.h1.a1', '150.i1.a1', '150.j1.a1', '150.j1.b1', '250.b1.a1', '375.a1.a1'], 'contains': ['1500.e1.a1', '2250.b1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [8021, -1, 1247, -1, 7509, -1, 7316, -1], 'generators': [5733, 4, 102], 'label': '9000.o.750.c1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '750.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997942
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '750.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '375.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['150.k1.a1', '150.l1.a1', '150.l1.b1', '150.l1.c1', '150.l1.d1', '150.m1.a1', '150.n1.a1', '250.c1.a1', '375.a1.a1'], 'contains': ['1500.e1.a1', '2250.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': [8700, -1, 2901, -1, 9095, -1, 8948, -1], 'generators': [3, 4, 6], 'label': '9000.o.750.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '750.d1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997943
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '750.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '250.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.o1.a1', '150.o1.a1', '250.b1.a1', '375.b1.a1'], 'contains': ['1500.f1.a1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [5375, -1, 297, -1, 2529, -1, 1524, -1], 'generators': [5733, 1200, 102], 'label': '9000.o.750.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '750.e1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68997944
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '750.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '750.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.p1.a1', '150.p1.a1', '250.c1.a1', '375.b1.a1'], 'contains': ['1500.f1.a1', '2250.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [7001, -1, 3298, -1, 2635, -1, 1588, -1], 'generators': [3, 6, 1200], 'label': '9000.o.750.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '750.f1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997945
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '750.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '250.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.q1.a1', '150.q1.a1', '250.b1.a1'], 'contains': ['1500.g1.a1', '2250.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 250, 'diagramx': [6036, -1, 153, -1, 2309, -1, 1461, -1], 'generators': [5733, 1204, 102], 'label': '9000.o.750.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '250.b1.a1', 'old_label': '750.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '750.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997946
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.b1.a1', '300.a1.a1', '300.d1.a1', '450.a1.a1'], 'contains': ['1800.a1.a1', '4500.a1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [891, -1, 8460, -1, 4341, -1, 2388, -1], 'generators': [60, 24], 'label': '9000.o.900.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '900.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997947
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.c1.a1', '300.b1.a1', '450.b1.a1'], 'contains': ['1800.b1.a1', '4500.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3617, -1, 7882, -1, 5214, -1, 4630, -1], 'generators': [60, 384], 'label': '9000.o.900.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '900.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997948
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.c1.b1', '300.b1.b1', '450.b1.b1'], 'contains': ['1800.b1.b1', '4500.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3617, -1, 7724, -1, 5214, -1, 4147, -1], 'generators': [60, 744], 'label': '9000.o.900.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '900.b1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997949
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.c1.d1', '300.b1.c1', '450.b1.c1'], 'contains': ['1800.b1.c1', '4500.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3617, -1, 7928, -1, 5214, -1, 4210, -1], 'generators': [60, 1104], 'label': '9000.o.900.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '900.b1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.b1.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997950
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '15.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['30.b1.a1', '30.g1.a1', '30.l1.a1', '45.b1.a1', '75.a1.a1', '75.e1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7058, -1, 2675, -1, 7786, -1, 7600, -1], 'generators': [1203, 5760, 4, 6, 60, 24], 'label': '9000.o.15.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '15.b1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997951
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.c1.c1', '300.b1.d1', '450.b1.d1'], 'contains': ['1800.b1.d1', '4500.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3617, -1, 8081, -1, 5214, -1, 4394, -1], 'generators': [60, 1464], 'label': '9000.o.900.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '900.b1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.b1.d1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997952
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.a1.a1', '180.d1.a1', '300.c1.a1', '450.c1.a1'], 'contains': ['1800.c1.a1', '4500.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1299, -1, 7646, -1, 4936, -1, 3958, -1], 'generators': [60, 360], 'label': '9000.o.900.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '900.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997953
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.b1.a1', '180.c1.a1', '180.c1.b1', '180.c1.c1', '180.c1.d1', '180.d1.a1', '300.e1.a1', '450.d1.a1'], 'contains': ['1800.d1.a1', '4500.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2012, -1, 9401, -1, 4676, -1, 2759, -1], 'generators': [60, 5760], 'label': '9000.o.900.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '900.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.d1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997954
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.a1', '180.f1.a1', '180.f1.b1', '180.f1.c1', '180.f1.d1', '180.g1.a1', '300.f1.a1', '450.d1.a1'], 'contains': ['1800.d1.a1', '4500.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4105, -1, 9102, -1, 3738, -1, 3460, -1], 'generators': [114, 5760], 'label': '9000.o.900.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '900.e1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997955
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.e1.a1', '180.h1.a1', '300.g1.a1', '300.j1.a1', '450.a1.a1'], 'contains': ['1800.a1.a1', '4500.b1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [2281, -1, 7523, -1, 3395, -1, 2567, -1], 'generators': [114, 24], 'label': '9000.o.900.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '900.f1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.f1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997956
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.f1.a1', '180.h1.a1', '300.h1.a1', '450.b1.a1'], 'contains': ['1800.b1.a1', '4500.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5097, -1, 6551, -1, 3933, -1, 5082, -1], 'generators': [114, 384], 'label': '9000.o.900.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '900.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.g1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997957
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.f1.b1', '180.h1.a1', '300.h1.b1', '450.b1.b1'], 'contains': ['1800.b1.b1', '4500.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5097, -1, 6493, -1, 3933, -1, 4783, -1], 'generators': [114, 744], 'label': '9000.o.900.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '900.g1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.g1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997958
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.f1.d1', '180.h1.a1', '300.h1.c1', '450.b1.c1'], 'contains': ['1800.b1.c1', '4500.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5097, -1, 6875, -1, 3933, -1, 4869, -1], 'generators': [114, 1104], 'label': '9000.o.900.g1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '900.g1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.g1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997959
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.f1.c1', '180.h1.a1', '300.h1.d1', '450.b1.d1'], 'contains': ['1800.b1.d1', '4500.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5097, -1, 6915, -1, 3933, -1, 4938, -1], 'generators': [114, 1464], 'label': '9000.o.900.g1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '900.g1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.g1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997960
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '300.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.g1.a1', '180.h1.a1', '300.i1.a1', '450.c1.a1'], 'contains': ['1800.c1.a1', '4500.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3261, -1, 6336, -1, 3821, -1, 4708, -1], 'generators': [114, 360], 'label': '9000.o.900.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '900.h1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.h1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997961
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '15.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['30.c1.a1', '30.i1.a1', '30.m1.a1', '45.c1.a1', '75.b1.a1', '75.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9305, -1, 3051, -1, 8536, -1, 8339, -1], 'generators': [1203, 5760, 4, 6, 60, 6144], 'label': '9000.o.15.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '15.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997962
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.a1', '180.j1.a1', '300.k1.a1', '300.p1.a1', '300.q1.a1', '450.a1.a1', '450.e1.a1', '450.j1.a1'], 'contains': ['1800.a1.a1', '4500.c1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3969, -1, 4575, -1, 6418, -1, 5981, -1], 'generators': [6, 24], 'label': '9000.o.900.i1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '900.i1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.i1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997963
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.a1', '180.k1.a1', '180.l1.a1', '180.l1.b1', '300.l1.a1', '450.b1.a1', '450.f1.a1', '450.k1.a1'], 'contains': ['1800.b1.a1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7842, -1, 3955, -1, 7102, -1, 7081, -1], 'generators': [6, 384], 'label': '9000.o.900.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.a1', 'old_label': '900.j1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.j1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997964
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.a1', '180.k1.b1', '180.l1.b1', '180.l1.c1', '300.l1.b1', '450.b1.b1', '450.f1.b1', '450.k1.b1'], 'contains': ['1800.b1.b1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7842, -1, 3786, -1, 7102, -1, 6926, -1], 'generators': [6, 744], 'label': '9000.o.900.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.b1', 'old_label': '900.j1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.j1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997965
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.a1', '180.k1.b1', '180.l1.a1', '180.l1.d1', '300.l1.c1', '450.b1.c1', '450.f1.c1', '450.k1.c1'], 'contains': ['1800.b1.c1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7842, -1, 4035, -1, 7102, -1, 6978, -1], 'generators': [6, 1104], 'label': '9000.o.900.j1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.c1', 'old_label': '900.j1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.j1.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997966
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.a1', '180.k1.a1', '180.l1.c1', '180.l1.d1', '300.l1.d1', '450.b1.d1', '450.f1.d1', '450.k1.d1'], 'contains': ['1800.b1.d1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [7842, -1, 4190, -1, 7102, -1, 7029, -1], 'generators': [6, 1464], 'label': '9000.o.900.j1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.b1.d1', 'old_label': '900.j1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.j1.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997967
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.i1.a1', '180.k1.a1', '180.k1.b1', '180.m1.a1', '300.m1.a1', '450.c1.a1', '450.g1.a1', '450.l1.a1'], 'contains': ['1800.c1.a1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [4611, -1, 3749, -1, 6744, -1, 6875, -1], 'generators': [6, 360], 'label': '9000.o.900.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.c1.a1', 'old_label': '900.k1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.k1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997968
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.j1.a1', '180.l1.a1', '180.l1.b1', '180.l1.c1', '180.l1.d1', '180.m1.a1', '300.n1.a1', '450.d1.a1', '450.h1.a1', '450.m1.a1'], 'contains': ['1800.d1.a1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [5671, -1, 5089, -1, 6601, -1, 6721, -1], 'generators': [6, 3960], 'label': '9000.o.900.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '900.l1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.l1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997969
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.j1.a1', '180.k1.a1', '180.k1.b1', '180.l1.a1', '180.l1.c1', '300.o1.a1', '450.i1.a1'], 'contains': ['1800.e1.a1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [7415, -1, 4484, -1, 6886, -1, 6823, -1], 'generators': [6, 2184], 'label': '9000.o.900.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.j1.a1', 'old_label': '900.m1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.m1.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997970
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '900.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['180.j1.a1', '180.k1.a1', '180.k1.b1', '180.l1.b1', '180.l1.d1', '300.o1.b1', '450.i1.b1'], 'contains': ['1800.e1.b1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 150, 'diagramx': [7415, -1, 4743, -1, 6886, -1, 6772, -1], 'generators': [6, 2544], 'label': '9000.o.900.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.j1.b1', 'old_label': '900.m1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '900.m1.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 68997971
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '50.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '200.a1.a1', '500.a1.a1', '500.b1.a1', '500.c1.a1'], 'contains': ['3000.a1.a1', '3000.b1.a1', '3000.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [325, -1, 8711, -1, 1376, -1, 856, -1], 'generators': [4, 1200], 'label': '9000.o.1000.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '1000.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68997972
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '15.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['30.c1.b1', '30.i1.b1', '30.m1.b1', '45.c1.b1', '75.b1.b1', '75.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9305, -1, 3886, -1, 8536, -1, 7839, -1], 'generators': [1203, 5760, 4, 6, 60, 3264], 'label': '9000.o.15.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '15.c1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.c1.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997973
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1125.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '375.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['225.a1.a1', '225.b1.a1', '225.b1.b1', '225.b1.c1', '225.b1.d1', '225.c1.a1', '225.d1.a1', '375.a1.a1', '375.b1.a1'], 'contains': ['2250.a1.a1', '2250.b1.a1', '2250.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': [8001, -1, 2193, -1, 8539, -1, 8599, -1], 'generators': [1203, 60], 'label': '9000.o.1125.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '1125.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1125.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997974
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1500.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.a1.a1', '300.b1.a1', '300.b1.b1', '300.b1.c1', '300.b1.d1', '300.c1.a1', '300.e1.a1', '500.a1.a1', '750.a1.a1'], 'contains': ['3000.a1.a1', '4500.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1571, -1, 8041, -1, 4601, -1, 3838, -1], 'generators': [60, 4], 'label': '9000.o.1500.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '1500.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997975
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1500.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '150.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '300.d1.a1', '500.a1.a1', '750.b1.a1'], 'contains': ['3000.b1.a1', '4500.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [26, -1, 9036, -1, 1662, -1, 911, -1], 'generators': [60, 1200], 'label': '9000.o.1500.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '1500.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997976
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1500.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '75.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.f1.a1', '300.g1.a1', '300.h1.a1', '300.h1.b1', '300.h1.c1', '300.h1.d1', '300.i1.a1', '500.b1.a1', '750.a1.a1'], 'contains': ['3000.a1.a1', '4500.b1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3434, -1, 6785, -1, 3503, -1, 4514, -1], 'generators': [114, 4], 'label': '9000.o.1500.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '1500.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997977
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1500.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '750.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.i1.a1', '300.j1.a1', '500.b1.a1', '750.b1.a1'], 'contains': ['3000.b1.a1', '4500.b1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [650, -1, 8550, -1, 1456, -1, 1026, -1], 'generators': [114, 1200], 'label': '9000.o.1500.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '1500.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 68997978
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1500.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '125.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['300.k1.a1', '300.l1.a1', '300.l1.b1', '300.l1.c1', '300.l1.d1', '300.m1.a1', '300.n1.a1', '300.o1.a1', '300.o1.b1', '500.c1.a1', '750.a1.a1', '750.c1.a1', '750.d1.a1'], 'contains': ['3000.a1.a1', '4500.c1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [5208, -1, 4364, -1, 6526, -1, 6266, -1], 'generators': [6, 4], 'label': '9000.o.1500.e1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '1500.e1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997979
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1500.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '250.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.p1.a1', '300.p1.a1', '500.c1.a1', '750.b1.a1', '750.e1.a1', '750.f1.a1'], 'contains': ['3000.b1.a1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [2636, -1, 5048, -1, 2197, -1, 1319, -1], 'generators': [6, 1200], 'label': '9000.o.1500.f1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '1500.f1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68997980
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1500.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '250.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.q1.a1', '300.q1.a1', '500.c1.a1', '750.g1.a1'], 'contains': ['3000.c1.a1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 250, 'diagramx': [2803, -1, 967, -1, 1938, -1, 1245, -1], 'generators': [6, 1204], 'label': '9000.o.1500.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '250.b1.a1', 'old_label': '1500.g1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1500.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997981
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1800.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['360.b1.a1', '360.c1.a1', '600.a1.a1', '600.f1.a1', '600.g1.a1', '900.a1.a1', '900.f1.a1', '900.i1.a1'], 'contains': ['9000.a1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1292, 4513, 8361, 5017, 4341, 5213, 2509, 5177], 'generators': [24], 'label': '9000.o.1800.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1800.a1.a1', 'normal_contained_in': ['72.a1.a1', '600.a1.a1'], 'normal_contains': ['9000.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1800.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': '4.1', 'quotient_action_kernel': '450.20', 'quotient_action_kernel_order': 450, 'quotient_fusion': None, 'short_label': '1800.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997982
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.b1.a1', '360.d1.a1', '360.e1.a1', '360.e1.b1', '600.b1.a1', '900.b1.a1', '900.g1.a1', '900.j1.a1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4854, -1, 7010, -1, 5078, -1, 4457, -1], 'generators': [384], 'label': '9000.o.1800.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '1800.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997983
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '15.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['30.c1.c1', '30.i1.c1', '30.m1.c1', '45.c1.c1', '75.b1.d1', '75.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9305, -1, 2944, -1, 8536, -1, 8220, -1], 'generators': [1203, 5760, 4, 6, 60, 4704], 'label': '9000.o.15.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '15.c1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.c1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997984
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.b1.a1', '360.d1.b1', '360.e1.b1', '360.e1.c1', '600.b1.b1', '900.b1.b1', '900.g1.b1', '900.j1.b1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4854, -1, 6945, -1, 5078, -1, 4050, -1], 'generators': [744], 'label': '9000.o.1800.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '1800.b1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997985
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.b1.a1', '360.d1.b1', '360.e1.a1', '360.e1.d1', '600.b1.c1', '900.b1.c1', '900.g1.c1', '900.j1.c1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4854, -1, 7061, -1, 5078, -1, 4101, -1], 'generators': [1104], 'label': '9000.o.1800.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '1800.b1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.b1.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997986
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1800.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.b1.a1', '360.d1.a1', '360.e1.c1', '360.e1.d1', '600.b1.d1', '900.b1.d1', '900.g1.d1', '900.j1.d1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4854, -1, 7175, -1, 5078, -1, 4331, -1], 'generators': [1464], 'label': '9000.o.1800.b1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '1800.b1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.b1.d1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997987
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1800.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '360.b1.a1', '360.d1.a1', '360.d1.b1', '600.c1.a1', '900.c1.a1', '900.h1.a1', '900.k1.a1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1807, -1, 6293, -1, 4804, -1, 3998, -1], 'generators': [360], 'label': '9000.o.1800.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '1800.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997988
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1800.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.a1.a1', '360.c1.a1', '360.e1.a1', '360.e1.b1', '360.e1.c1', '360.e1.d1', '600.d1.a1', '900.d1.a1', '900.e1.a1', '900.l1.a1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3270, -1, 9347, -1, 4522, -1, 3399, -1], 'generators': [3960], 'label': '9000.o.1800.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '360.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '1800.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997989
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1800.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.c1.a1', '360.d1.a1', '360.d1.b1', '360.e1.a1', '360.e1.c1', '600.e1.a1', '900.m1.a1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3841, -1, 7100, -1, 5238, -1, 3751, -1], 'generators': [2184], 'label': '9000.o.1800.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '1800.e1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997990
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '1800.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['360.c1.a1', '360.d1.a1', '360.d1.b1', '360.e1.b1', '360.e1.d1', '600.e1.b1', '900.m1.b1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3841, -1, 7138, -1, 5238, -1, 3563, -1], 'generators': [2544], 'label': '9000.o.1800.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '1800.e1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1800.e1.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 68997991
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '2250.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '375.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.a1.a1', '450.b1.a1', '450.b1.b1', '450.b1.c1', '450.b1.d1', '450.c1.a1', '450.d1.a1', '750.a1.a1', '750.b1.a1', '1125.a1.a1'], 'contains': ['4500.a1.a1', '4500.b1.a1', '4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': [4418, -1, 5451, -1, 5615, -1, 5539, -1], 'generators': [6, 60], 'label': '9000.o.2250.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '2250.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2250.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997992
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '2250.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '125.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.e1.a1', '450.f1.a1', '450.f1.b1', '450.f1.c1', '450.f1.d1', '450.g1.a1', '450.h1.a1', '450.i1.a1', '450.i1.b1', '750.c1.a1', '750.e1.a1', '750.g1.a1', '1125.a1.a1'], 'contains': ['4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [7472, -1, 1348, -1, 7551, -1, 7536, -1], 'generators': [5733], 'label': '9000.o.2250.b1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '2250.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2250.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997993
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '2250.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '375.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['450.j1.a1', '450.k1.a1', '450.k1.b1', '450.k1.c1', '450.k1.d1', '450.l1.a1', '450.m1.a1', '750.d1.a1', '750.f1.a1', '1125.a1.a1'], 'contains': ['4500.c1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 375, 'diagramx': [7893, -1, 2662, -1, 9053, -1, 8948, -1], 'generators': [3], 'label': '9000.o.2250.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '375.a1.a1', 'old_label': '2250.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2250.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997994
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '15.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['30.c1.d1', '30.i1.d1', '30.m1.d1', '45.c1.d1', '75.b1.c1', '75.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9305, -1, 2856, -1, 8536, -1, 7958, -1], 'generators': [1203, 5760, 4, 6, 60, 7584], 'label': '9000.o.15.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '15.c1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.c1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68997995
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '3000.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['600.a1.a1', '600.b1.a1', '600.b1.b1', '600.b1.c1', '600.b1.d1', '600.c1.a1', '600.d1.a1', '600.e1.a1', '600.e1.b1', '1000.a1.a1', '1500.a1.a1', '1500.c1.a1', '1500.e1.a1'], 'contains': ['9000.a1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2969, 3899, 7424, 5706, 4601, 4685, 3895, 4647], 'generators': [4], 'label': '9000.o.3000.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '3000.a1.a1', 'normal_contained_in': ['120.a1.a1', '600.a1.a1'], 'normal_contains': ['9000.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3000.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3000.bf', 'quotient_action_kernel_order': 3000, 'quotient_fusion': None, 'short_label': '3000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997996
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '3000.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '50.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '600.f1.a1', '1000.a1.a1', '1500.b1.a1', '1500.d1.a1', '1500.f1.a1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [277, -1, 8711, -1, 1605, -1, 968, -1], 'generators': [1200], 'label': '9000.o.3000.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1.a1', 'old_label': '3000.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3000.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68997997
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '3000.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '50.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.g1.a1', '600.g1.a1', '1000.a1.a1', '1500.g1.a1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [462, -1, 6114, -1, 1376, -1, 856, -1], 'generators': [1204], 'label': '9000.o.3000.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.b1.a1', 'old_label': '3000.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3000.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997998
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '4500.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '15.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.a1.a1', '900.b1.a1', '900.b1.b1', '900.b1.c1', '900.b1.d1', '900.c1.a1', '900.d1.a1', '1500.a1.a1', '1500.b1.a1', '2250.a1.a1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1474, -1, 7928, -1, 4676, -1, 3947, -1], 'generators': [60], 'label': '9000.o.4500.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '4500.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68997999
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '4500.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '75.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.e1.a1', '900.f1.a1', '900.g1.a1', '900.g1.b1', '900.g1.c1', '900.g1.d1', '900.h1.a1', '1500.c1.a1', '1500.d1.a1', '2250.a1.a1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 75, 'diagramx': [3407, -1, 6866, -1, 3780, -1, 4708, -1], 'generators': [114], 'label': '9000.o.4500.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '75.e1.a1', 'old_label': '4500.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68998000
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '4500.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '125.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['900.i1.a1', '900.j1.a1', '900.j1.b1', '900.j1.c1', '900.j1.d1', '900.k1.a1', '900.l1.a1', '900.m1.a1', '900.m1.b1', '1500.e1.a1', '1500.f1.a1', '1500.g1.a1', '2250.a1.a1', '2250.b1.a1', '2250.c1.a1'], 'contains': ['9000.a1.a1'], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 125, 'diagramx': [5132, -1, 4125, -1, 6563, -1, 6798, -1], 'generators': [6], 'label': '9000.o.4500.c1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '125.a1.a1', 'old_label': '4500.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4500.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68998001
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '9000.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': ['1800.a1.a1', '1800.b1.a1', '1800.b1.b1', '1800.b1.c1', '1800.b1.d1', '1800.c1.a1', '1800.d1.a1', '1800.e1.a1', '1800.e1.b1', '3000.a1.a1', '3000.b1.a1', '3000.c1.a1', '4500.a1.a1', '4500.b1.a1', '4500.c1.a1'], 'contains': [], 'core': '9000.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2969, 3899, 7100, 5706, 4601, 4685, 3947, 4647], 'generators': [], 'label': '9000.o.9000.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '9000.a1.a1', 'normal_contained_in': ['360.a1.a1', '1800.a1.a1', '3000.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '9000.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9000.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68998002
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '15.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '5.a1.a1'], 'contains': ['30.d1.a1', '30.j1.a1', '30.n1.a1', '45.d1.a1', '75.c1.a1', '75.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8399, -1, 2769, -1, 7959, -1, 7719, -1], 'generators': [1203, 1800, 4, 6, 60, 360], 'label': '9000.o.15.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '15.d1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.d1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998003
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '15.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.e1.a1', '30.o1.a1', '30.p1.a1', '45.d1.a1', '375.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [6221, -1, 1931, -1, 3139, -1, 1903, -1], 'generators': [3, 1800, 6, 1200, 60, 5760], 'label': '9000.o.15.e1.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.e1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15.e1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68998004
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': ['500.a1.a1', '500.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.c1.a1', '6.g1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '90.e1.a1', '90.f1.a1', '90.g1.a1', '90.g1.b1', '90.h1.a1', '90.h1.b1', '90.h1.c1', '90.h1.d1', '90.i1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7474, 7706, 807, 2246, 7173, 7952, 7489, 7936], 'generators': [5733, 24, 360, 102, 1800], 'label': '9000.o.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.b1.a1', '6.c1.a1'], 'normal_contains': ['36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3000.bf'}
  • id: 68998005
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.e1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '90.a1.a1', '90.b1.a1', '90.c1.a1', '90.c1.b1', '90.c1.c1', '90.c1.d1', '90.d1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4144, -1, 6541, -1, 5456, -1, 4573, -1], 'generators': [6, 24, 360, 60, 1800], 'label': '9000.o.18.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.168'}
  • id: 68998023
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.e1.a1'], 'contains': ['60.a1.a1', '60.i1.a1', '60.p1.a1', '90.d1.a1', '750.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1491, -1, 6370, -1, 1686, -1, 890, -1], 'generators': [6, 1200, 7560, 60, 1800], 'label': '9000.o.30.e1.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.e1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.e1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68998006
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': ['4500.a1.a1', '4500.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '6.d1.a1', '6.f1.a1', '10.c1.a1', '50.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6995, 6171, 4212, 3657, 3332, 6561, 2301, 5442], 'generators': [3, 5760, 6, 1200, 4, 1800, 24], 'label': '9000.o.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '3000.bf', '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': '3000.bf'}
  • id: 68998007
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '90.j1.a1', '90.k1.a1', '90.l1.a1', '90.l1.b1', '90.l1.c1', '90.l1.d1', '90.m1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7949, -1, 3441, -1, 9298, -1, 9270, -1], 'generators': [3, 24, 3960, 6, 1800], 'label': '9000.o.18.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.168'}
  • id: 68998008
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': ['450.j1.a1', '450.k1.d1', '450.k1.c1', '450.k1.b1', '450.k1.a1', '450.e1.a1', '450.f1.d1', '450.f1.c1', '450.f1.b1', '450.f1.a1', '450.i1.a1', '450.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '60.a1.a1', '60.e1.a1', '500.a1.a1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [960, 741, 9348, 9157, 1036, 619, 378, 622], 'generators': [60, 1200, 5760, 4, 1800], 'label': '9000.o.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['40.a1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '3000.bf', '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': '600.151'}
  • id: 68998009
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '60.h1.a1', '60.i1.a1', '500.b1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [1275, -1, 8963, -1, 461, -1, 675, -1], 'generators': [114, 1200, 3960, 4, 1800], 'label': '9000.o.20.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '3000.bf', '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': '600.151'}
  • id: 68998010
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.a1.a1', '10.b1.a1', '10.c1.a1'], 'contains': ['40.a1.a1', '60.o1.a1', '60.p1.a1', '60.q1.a1', '500.c1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [2222, -1, 4930, -1, 2001, -1, 1106, -1], 'generators': [6, 1200, 360, 4, 1800], 'label': '9000.o.20.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '3000.bf', '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': '600.151'}
  • id: 68998011
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': ['375.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1', '12.e1.a1', '12.f1.a1'], 'contains': ['72.a1.a1', '120.a1.a1', '120.c1.a1', '120.d1.a1', '120.e1.a1', '120.e1.b1', '120.f1.a1', '120.f1.b1', '120.f1.c1', '120.f1.d1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2717, 4996, 9171, 4765, 4595, 5645, 3032, 5611], 'generators': [4, 360, 1800, 24], 'label': '9000.o.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.c1.a1'], 'normal_contains': ['72.a1.a1', '120.a1.a1', '600.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': '24.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.5'}
  • id: 68998012
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': ['375.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.d1.a1'], 'contains': ['72.a1.a1', '120.b1.a1', '600.f1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [700, 3364, 8705, 6327, 846, 4282, 464, 4242], 'generators': [1200, 7560, 1800, 24], 'label': '9000.o.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.d1.a1'], 'normal_contains': ['72.a1.a1', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': '8.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68998013
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.g1.a1'], 'contains': ['72.a1.a1', '120.g1.a1', '600.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1371, -1, 5845, -1, 88, -1, 61, -1], 'generators': [1204, 7560, 1800, 24], 'label': '9000.o.24.c1.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': '24.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '300.24'}
  • id: 68998014
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['50.a1.a1', '50.b1.a1', '50.c1.a1', '75.a1.a1', '75.d1.a1', '125.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6623, -1, 1044, -1, 2887, -1, 2076, -1], 'generators': [3, 24, 4, 6, 60, 1200], 'label': '9000.o.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': '3000.bf', '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': '120.36'}
  • id: 68998015
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '15.a1.a1'], 'contains': ['60.b1.a1', '60.j1.a1', '60.k1.a1', '90.a1.a1', '150.a1.a1', '150.b1.a1', '150.b1.b1', '150.b1.c1', '150.b1.d1', '150.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4255, -1, 5269, -1, 5630, -1, 5053, -1], 'generators': [6, 4, 24, 60, 360], 'label': '9000.o.30.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '3000.bf', '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': '100.11'}
  • id: 68998016
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '15.b1.a1'], 'contains': ['60.c1.a1', '60.f1.a1', '60.l1.a1', '90.b1.a1', '150.a1.a1', '150.e1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3837, -1, 5812, -1, 5122, -1, 4344, -1], 'generators': [6, 4, 24, 60, 5760], 'label': '9000.o.30.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.b1.a1', 'projective_image': '3000.bf', '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': '200.42'}
  • id: 68998017
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': ['3000.a1.a1', '3000.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.c1.a1', '6.d1.a1', '9.a1.a1', '15.e1.a1', '75.d1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6295, 5136, 1993, 3682, 3076, 5000, 1988, 7009], 'generators': [3, 5760, 6, 1200, 60, 1800, 24], 'label': '9000.o.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.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '9000.o', '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': '3000.bf'}
  • id: 68998018
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '15.c1.a1'], 'contains': ['60.d1.a1', '60.g1.a1', '60.n1.a1', '90.c1.a1', '150.b1.a1', '150.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5935, -1, 6195, -1, 5816, -1, 4916, -1], 'generators': [6, 4, 3624, 60, 5760], 'label': '9000.o.30.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '30.c1.a1', 'projective_image': '3000.bf', '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': '200.42'}
  • id: 68998019
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '15.c1.b1'], 'contains': ['60.d1.b1', '60.g1.b1', '60.n1.b1', '90.c1.b1', '150.b1.b1', '150.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5935, -1, 6688, -1, 5816, -1, 4457, -1], 'generators': [6, 4, 7224, 60, 5760], 'label': '9000.o.30.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '30.c1.b1', 'projective_image': '3000.bf', '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': '200.42'}
  • id: 68998020
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '15.c1.c1'], 'contains': ['60.d1.c1', '60.g1.c1', '60.n1.c1', '90.c1.c1', '150.b1.d1', '150.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5935, -1, 6278, -1, 5816, -1, 4803, -1], 'generators': [6, 4, 5424, 60, 5760], 'label': '9000.o.30.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '30.c1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998021
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '15.c1.d1'], 'contains': ['60.d1.d1', '60.g1.d1', '60.n1.d1', '90.c1.d1', '150.b1.c1', '150.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [5935, -1, 6040, -1, 5816, -1, 4690, -1], 'generators': [6, 4, 1824, 60, 5760], 'label': '9000.o.30.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '30.c1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.c1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998022
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '10.a1.a1', '15.d1.a1'], 'contains': ['60.e1.a1', '60.h1.a1', '60.o1.a1', '90.d1.a1', '150.c1.a1', '150.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4540, -1, 6441, -1, 5286, -1, 4231, -1], 'generators': [6, 4, 360, 60, 1800], 'label': '9000.o.30.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '30.d1.a1', 'projective_image': '3000.bf', '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': '200.42'}
  • id: 68998024
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.a1.a1'], 'contains': ['60.k1.a1', '90.e1.a1', '150.f1.a1', '150.g1.a1', '150.g1.b1', '150.g1.c1', '150.g1.d1', '150.h1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [6464, -1, 1388, -1, 7346, -1, 7370, -1], 'generators': [5733, 102, 24, 4, 360], 'label': '9000.o.30.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.f1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.f1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68998025
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.b1.a1'], 'contains': ['60.l1.a1', '90.f1.a1', '150.f1.a1', '150.i1.a1', '150.j1.a1', '150.j1.b1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8584, -1, 1491, -1, 7001, -1, 6429, -1], 'generators': [5733, 102, 24, 4, 3960], 'label': '9000.o.30.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.g1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.g1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998026
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['60.m1.a1', '90.g1.a1', '150.g1.a1', '150.g1.d1', '150.h1.a1', '150.j1.a1', '150.j1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8327, -1, 1009, -1, 7738, -1, 6698, -1], 'generators': [5733, 102, 1824, 4, 360], 'label': '9000.o.30.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.h1.a1', 'old_label': '30.h1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.h1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68998027
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['60.m1.b1', '90.g1.b1', '150.g1.b1', '150.g1.c1', '150.h1.a1', '150.j1.a1', '150.j1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 30, 'diagramx': [8327, -1, 697, -1, 7738, -1, 6564, -1], 'generators': [5733, 102, 3624, 4, 360], 'label': '9000.o.30.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '30.h1.b1', 'old_label': '30.h1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.h1.b1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68998028
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.e1.a1', '6.f1.a1', '9.a1.a1', '15.a1.a1', '15.b1.a1', '15.c1.a1', '15.c1.b1', '15.c1.c1', '15.c1.d1', '15.d1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7283, -1, 2935, -1, 7959, -1, 7898, -1], 'generators': [1203, 360, 4, 6, 60, 1800, 24], 'label': '9000.o.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1000.168'}
  • id: 68998029
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.c1.a1'], 'contains': ['60.n1.a1', '90.h1.a1', '150.g1.a1', '150.g1.c1', '150.i1.a1', '150.j1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9003, -1, 2292, -1, 7542, -1, 7236, -1], 'generators': [5733, 102, 7224, 4, 3960], 'label': '9000.o.30.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '30.i1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.i1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998030
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.c1.b1'], 'contains': ['60.n1.b1', '90.h1.b1', '150.g1.a1', '150.g1.b1', '150.i1.a1', '150.j1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9003, -1, 2443, -1, 7542, -1, 6833, -1], 'generators': [5733, 102, 5424, 4, 3960], 'label': '9000.o.30.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '30.i1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.i1.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998031
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.c1.c1'], 'contains': ['60.n1.c1', '90.h1.c1', '150.g1.b1', '150.g1.d1', '150.i1.a1', '150.j1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9003, -1, 1964, -1, 7542, -1, 7101, -1], 'generators': [5733, 102, 1824, 4, 3960], 'label': '9000.o.30.i1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '30.i1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.i1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998032
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '15.c1.d1'], 'contains': ['60.n1.d1', '90.h1.d1', '150.g1.c1', '150.g1.d1', '150.i1.a1', '150.j1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9003, -1, 1695, -1, 7542, -1, 6967, -1], 'generators': [5733, 102, 3624, 4, 3960], 'label': '9000.o.30.i1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '30.i1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.i1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998033
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.a1', '15.d1.a1'], 'contains': ['60.o1.a1', '90.i1.a1', '150.h1.a1', '150.i1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7051, -1, 1281, -1, 6805, -1, 6295, -1], 'generators': [5733, 102, 360, 4, 1800], 'label': '9000.o.30.j1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.j1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.j1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68998034
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '15.a1.a1'], 'contains': ['60.k1.a1', '90.j1.a1', '150.k1.a1', '150.l1.a1', '150.l1.b1', '150.l1.c1', '150.l1.d1', '150.m1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7996, -1, 3402, -1, 9465, -1, 9622, -1], 'generators': [3, 6, 24, 4, 7560], 'label': '9000.o.30.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '30.k1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.k1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68998035
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '15.b1.a1'], 'contains': ['60.l1.a1', '90.k1.a1', '150.k1.a1', '150.n1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7451, -1, 3865, -1, 8970, -1, 7925, -1], 'generators': [3, 6, 24, 4, 2160], 'label': '9000.o.30.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '30.l1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.l1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998036
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '15.c1.a1'], 'contains': ['60.n1.a1', '90.l1.a1', '150.l1.a1', '150.n1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9540, -1, 4059, -1, 9649, -1, 9496, -1], 'generators': [3, 6, 1104, 4, 2160], 'label': '9000.o.30.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '30.m1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.m1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998037
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '15.c1.b1'], 'contains': ['60.n1.b1', '90.l1.b1', '150.l1.b1', '150.n1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9540, -1, 4594, -1, 9649, -1, 9045, -1], 'generators': [3, 6, 384, 4, 2160], 'label': '9000.o.30.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '30.m1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.m1.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998038
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '15.c1.c1'], 'contains': ['60.n1.c1', '90.l1.c1', '150.l1.d1', '150.n1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9540, -1, 3952, -1, 9649, -1, 9377, -1], 'generators': [3, 6, 744, 4, 2160], 'label': '9000.o.30.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '30.m1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.m1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998039
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': ['2250.c1.a1', '2250.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.e1.a1', '20.a1.a1', '100.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [666, 1197, 9227, 8283, 1133, 1945, 552, 1910], 'generators': [60, 1800, 24, 1200, 4, 5760], 'label': '9000.o.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': '3000.bf', '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': '600.151'}
  • id: 68998040
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '15.c1.d1'], 'contains': ['60.n1.d1', '90.l1.d1', '150.l1.c1', '150.n1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [9540, -1, 3778, -1, 9649, -1, 9164, -1], 'generators': [3, 6, 1464, 4, 2160], 'label': '9000.o.30.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '30.m1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.m1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998041
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '10.c1.a1', '15.d1.a1'], 'contains': ['60.o1.a1', '90.m1.a1', '150.m1.a1', '150.n1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8830, -1, 4307, -1, 9143, -1, 8141, -1], 'generators': [3, 6, 3960, 4, 1800], 'label': '9000.o.30.n1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '30.n1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.n1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998042
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '10.b1.a1', '15.e1.a1'], 'contains': ['60.p1.a1', '90.i1.a1', '750.e1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [5642, -1, 1156, -1, 2677, -1, 1665, -1], 'generators': [5733, 102, 360, 1200, 1800], 'label': '9000.o.30.o1.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.o1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.o1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68998043
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '10.c1.a1', '15.e1.a1'], 'contains': ['60.p1.a1', '90.m1.a1', '750.f1.a1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 5, 'diagramx': [7686, -1, 4163, -1, 3430, -1, 2147, -1], 'generators': [3, 1200, 5760, 6, 1800], 'label': '9000.o.30.p1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '5.a1.a1', 'old_label': '30.p1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.p1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68998044
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '30.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '10.b1.a1'], 'contains': ['60.q1.a1', '90.i1.a1', '750.g1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6118, -1, 884, -1, 2290, -1, 1510, -1], 'generators': [5733, 102, 360, 1204, 1800], 'label': '9000.o.30.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1.a1', 'old_label': '30.q1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.q1.a1', 'subgroup_fusion': None, 'weyl_group': '300.24'}
  • id: 68998045
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.d1.a1', '12.g1.a1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'contains': ['72.a1.a1', '180.i1.a1', '180.j1.a1', '180.k1.a1', '180.k1.b1', '180.l1.a1', '180.l1.b1', '180.l1.c1', '180.l1.d1', '180.m1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5021, 6303, 4505, 3514, 6443, 6736, 6432, 6707], 'generators': [6, 360, 1800, 24], 'label': '9000.o.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.c1.a1', '12.d1.a1', '18.a1.a1'], 'normal_contains': ['72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3000.bf'}
  • id: 68998046
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.e1.a1', '18.b1.a1'], 'contains': ['72.a1.a1', '180.a1.a1', '180.b1.a1', '180.c1.a1', '180.c1.b1', '180.c1.c1', '180.c1.d1', '180.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1769, -1, 9771, -1, 4246, -1, 2441, -1], 'generators': [60, 1800, 5760, 24], 'label': '9000.o.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68998047
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.f1.a1', '18.b1.a1'], 'contains': ['72.a1.a1', '180.e1.a1', '180.f1.a1', '180.f1.b1', '180.f1.c1', '180.f1.d1', '180.g1.a1', '180.h1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3239, -1, 8286, -1, 3561, -1, 3158, -1], 'generators': [114, 24, 360, 1800], 'label': '9000.o.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.47'}
  • id: 68998048
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': ['225.a1.a1', '225.b1.a1', '225.b1.b1', '225.b1.c1', '225.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.g1.a1', '1000.a1.a1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1032, 2373, 9062, 7268, 534, 2905, 195, 2859], 'generators': [4, 7560, 1800, 1200], 'label': '9000.o.40.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['120.a1.a1', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '3000.bf', 'quotient_action_image': '8.2', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '600.151'}
  • id: 68998049
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '45.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1500.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.a1.a1'], 'contains': ['90.a1.a1', '90.e1.a1', '90.j1.a1', '225.a1.a1', '225.b1.a1', '225.b1.b1', '225.b1.c1', '225.b1.d1', '225.c1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7371, -1, 1854, -1, 8549, -1, 8919, -1], 'generators': [1203, 6, 24, 60, 360], 'label': '9000.o.45.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '45.a1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.a1.a1', 'subgroup_fusion': None, 'weyl_group': '100.11'}
  • id: 68998050
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': ['2250.c1.a1', '2250.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '12.f1.a1', '20.b1.a1', '100.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1667, 2952, 8737, 6604, 748, 3410, 809, 3381], 'generators': [114, 1800, 1200, 24, 4, 3960], 'label': '9000.o.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '3000.bf', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3000.bf'}
  • id: 68998051
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '45.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.b1.a1'], 'contains': ['90.b1.a1', '90.f1.a1', '90.k1.a1', '225.a1.a1', '225.d1.a1'], 'core': '1800.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [7235, -1, 2073, -1, 8121, -1, 7670, -1], 'generators': [1203, 6, 24, 60, 5760], 'label': '9000.o.45.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '45.b1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.b1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998052
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '45.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.c1.a1'], 'contains': ['90.c1.a1', '90.h1.a1', '90.l1.a1', '225.b1.a1', '225.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': '45T473', 'count': 15, 'diagramx': [9409, -1, 2770, -1, 8694, -1, 8625, -1], 'generators': [1203, 6, 6144, 60, 5760], 'label': '9000.o.45.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '45.c1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.c1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998053
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '45.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.c1.b1'], 'contains': ['90.c1.b1', '90.h1.b1', '90.l1.b1', '225.b1.b1', '225.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': '45T473', 'count': 15, 'diagramx': [9409, -1, 3172, -1, 8694, -1, 8233, -1], 'generators': [1203, 6, 3264, 60, 5760], 'label': '9000.o.45.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '45.c1.b1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.c1.b1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998054
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '45.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.c1.c1'], 'contains': ['90.c1.c1', '90.h1.c1', '90.l1.c1', '225.b1.d1', '225.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': '45T473', 'count': 15, 'diagramx': [9409, -1, 2635, -1, 8694, -1, 8559, -1], 'generators': [1203, 6, 4704, 60, 5760], 'label': '9000.o.45.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.c1', 'old_label': '45.c1.c1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.c1.c1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998055
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '45.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.c1.d1'], 'contains': ['90.c1.d1', '90.h1.d1', '90.l1.d1', '225.b1.c1', '225.d1.a1'], 'core': '9000.a1.a1', 'coset_action_label': '45T473', 'count': 15, 'diagramx': [9409, -1, 2219, -1, 8694, -1, 8397, -1], 'generators': [1203, 6, 7584, 60, 5760], 'label': '9000.o.45.c1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.d1', 'old_label': '45.c1.d1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.c1.d1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998056
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '45.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '15.d1.a1', '15.e1.a1'], 'contains': ['90.d1.a1', '90.i1.a1', '90.m1.a1', '225.c1.a1', '225.d1.a1'], 'core': '360.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [8064, -1, 1555, -1, 8025, -1, 7736, -1], 'generators': [1203, 6, 360, 60, 1800], 'label': '9000.o.45.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.d1.a1', 'old_label': '45.d1.a1', 'projective_image': '9000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '45.d1.a1', 'subgroup_fusion': None, 'weyl_group': '200.42'}
  • id: 68998057
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '25.a1.a1'], 'contains': ['100.a1.a1', '100.b1.a1', '100.c1.a1', '150.a1.a1', '150.d1.a1', '250.a1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [1581, -1, 5316, -1, 1477, -1, 1276, -1], 'generators': [6, 4, 1200, 60, 24], 'label': '9000.o.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': '3000.bf', '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': '120.36'}
  • id: 68998058
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '25.a1.a1'], 'contains': ['100.c1.a1', '150.f1.a1', '150.o1.a1', '150.q1.a1', '250.b1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5736, -1, 291, -1, 2523, -1, 1770, -1], 'generators': [5733, 1200, 102, 4, 24], 'label': '9000.o.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': '3000.bf', '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': '40.12'}
  • id: 68998059
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '50.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '25.a1.a1'], 'contains': ['100.c1.a1', '150.k1.a1', '150.p1.a1', '250.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [7110, -1, 4089, -1, 3224, -1, 2288, -1], 'generators': [3, 6, 1200, 4, 24], 'label': '9000.o.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': '3000.bf', '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': '120.36'}
  • id: 68998060
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.a1.a1', 'complements': ['150.k1.a1', '150.l1.d1', '150.l1.c1', '150.l1.b1', '150.l1.a1', '150.f1.a1', '150.g1.d1', '150.g1.c1', '150.g1.b1', '150.g1.a1', '150.j1.a1', '150.j1.b1', '150.q1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.e1.a1'], 'contains': ['120.b1.a1', '180.d1.a1', '1500.b1.a1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [710, 1382, 9293, 8215, 1211, 1806, 329, 1755], 'generators': [60, 5760, 1800, 1200], 'label': '9000.o.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.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '9000.o', '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': '600.151'}
  • id: 68998061
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3000.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.c1.a1', '12.d1.a1', '12.g1.a1', '20.c1.a1', '100.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2233, 6689, 4901, 4714, 2001, 6744, 1357, 5596], 'generators': [6, 1800, 1200, 24, 4, 360], 'label': '9000.o.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3000.bf'}
  • id: 68998062
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '60.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.a1.a1'], 'contains': ['120.c1.a1', '180.a1.a1', '300.a1.a1', '300.b1.a1', '300.b1.b1', '300.b1.c1', '300.b1.d1', '300.c1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [1138, -1, 7522, -1, 4776, -1, 3979, -1], 'generators': [60, 24, 360, 4], 'label': '9000.o.60.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '3000.bf', '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: 68998063
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.b1.a1'], 'contains': ['120.d1.a1', '180.b1.a1', '300.a1.a1', '300.e1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1916, -1, 8191, -1, 4414, -1, 2326, -1], 'generators': [60, 24, 5760, 4], 'label': '9000.o.60.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '60.c1.a1', 'projective_image': '3000.bf', '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': '40.12'}
  • id: 68998064
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.c1.a1'], 'contains': ['120.f1.a1', '180.c1.a1', '300.b1.a1', '300.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3936, -1, 8595, -1, 4947, -1, 3393, -1], 'generators': [60, 3624, 5760, 4], 'label': '9000.o.60.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '60.d1.a1', 'projective_image': '3000.bf', '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': '40.12'}
  • id: 68998065
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.c1.b1'], 'contains': ['120.f1.b1', '180.c1.b1', '300.b1.b1', '300.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3936, -1, 9452, -1, 4947, -1, 2790, -1], 'generators': [60, 7224, 5760, 4], 'label': '9000.o.60.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '60.d1.b1', 'projective_image': '3000.bf', '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': '40.12'}
  • id: 68998066
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.c1.c1'], 'contains': ['120.f1.c1', '180.c1.c1', '300.b1.d1', '300.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3936, -1, 9101, -1, 4947, -1, 3276, -1], 'generators': [60, 5424, 5760, 4], 'label': '9000.o.60.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '60.d1.c1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.c1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68998067
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '30.c1.d1'], 'contains': ['120.f1.d1', '180.c1.d1', '300.b1.c1', '300.e1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3936, -1, 8403, -1, 4947, -1, 2907, -1], 'generators': [60, 1824, 5760, 4], 'label': '9000.o.60.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '60.d1.d1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.d1.d1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68998068
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '20.a1.a1', '30.d1.a1'], 'contains': ['120.a1.a1', '180.d1.a1', '300.c1.a1', '300.e1.a1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1645, -1, 9618, -1, 3908, -1, 2208, -1], 'generators': [60, 1800, 5760, 4], 'label': '9000.o.60.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '60.e1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.e1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68998069
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.b1.a1'], 'contains': ['120.d1.a1', '180.e1.a1', '300.f1.a1', '300.g1.a1'], 'core': '600.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [3100, -1, 7654, -1, 3218, -1, 2673, -1], 'generators': [114, 5760, 24, 4], 'label': '9000.o.60.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.b1.a1', 'old_label': '60.f1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.f1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68998070
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.c1.a1'], 'contains': ['120.f1.a1', '180.f1.a1', '300.f1.a1', '300.h1.a1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4885, -1, 8297, -1, 4079, -1, 3862, -1], 'generators': [114, 5760, 384, 4], 'label': '9000.o.60.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.a1', 'old_label': '60.g1.a1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 68998071
    {'ambient': '9000.o', 'aut_centralizer_order': None, 'aut_label': '60.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '600.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '30.c1.b1'], 'contains': ['120.f1.b1', '180.f1.b1', '300.f1.a1', '300.h1.b1'], 'core': '3000.a1.a1', 'coset_action_label': None, 'count': 15, 'diagramx': [4885, -1, 8956, -1, 4079, -1, 3511, -1], 'generators': [114, 5760, 744, 4], 'label': '9000.o.60.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '15.c1.b1', 'old_label': '60.g1.b1', 'projective_image': '3000.bf', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.g1.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}