Abstract group data - 12096.r

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 252, 'aut_gen_orders': [6, 36], 'aut_gens': [[1010031245, 566507649], [3006189485, 2558480538], [2486535263, 3554213169]], 'aut_group': '12096.r', 'aut_hash': 5927777241500214389, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12096, 'aut_permdeg': 88, 'aut_perms': [157040828995176290150131868067927840556572792950176851747617563324015506778110161581062201698523241432571843745176371029689292975571213, 94939144073226755007077166124183573489599896196307792850610715307677707328437635108624395851275976129990264105490711400951966018869475], 'aut_phi_ratio': 3.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [2, 63, 1, 2], [2, 126, 2, 1], [3, 56, 1, 1], [3, 84, 1, 2], [4, 2, 1, 1], [4, 126, 1, 1], [6, 56, 1, 1], [6, 84, 1, 2], [6, 112, 2, 1], [6, 168, 2, 2], [6, 252, 1, 4], [6, 504, 2, 2], [7, 216, 1, 1], [9, 168, 1, 3], [12, 112, 1, 1], [12, 168, 1, 2], [12, 504, 1, 2], [14, 216, 1, 1], [14, 432, 2, 1], [18, 168, 1, 3], [18, 336, 2, 3], [28, 432, 1, 1], [36, 336, 1, 3]], 'aut_supersolvable': False, 'aut_tex': 'D_4\\times {}^2G(2,3)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 126, 'autcentquo_group': '3024.r', 'autcentquo_hash': 5679810977767407995, 'autcentquo_nilpotent': False, 'autcentquo_order': 3024, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SL(2,8):C_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [2, 63, 2], [2, 126, 2], [3, 56, 1], [3, 84, 2], [4, 2, 1], [4, 126, 1], [6, 56, 1], [6, 84, 2], [6, 112, 2], [6, 168, 4], [6, 252, 4], [6, 504, 4], [7, 216, 1], [9, 168, 3], [12, 112, 1], [12, 168, 2], [12, 504, 2], [14, 216, 1], [14, 432, 2], [18, 168, 3], [18, 336, 6], [28, 432, 1], [36, 336, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '1008.880', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '504.156'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 18, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['1512.779', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [2, 63, 1, 2], [2, 126, 1, 2], [3, 56, 1, 1], [3, 84, 2, 1], [4, 2, 1, 1], [4, 126, 1, 1], [6, 56, 1, 1], [6, 84, 2, 1], [6, 112, 1, 2], [6, 168, 2, 2], [6, 252, 2, 2], [6, 504, 2, 2], [7, 216, 1, 1], [9, 168, 1, 1], [9, 168, 2, 1], [12, 112, 1, 1], [12, 168, 2, 1], [12, 504, 2, 1], [14, 216, 1, 1], [14, 432, 1, 2], [18, 168, 1, 1], [18, 168, 2, 1], [18, 336, 1, 2], [18, 336, 2, 2], [28, 432, 1, 1], [36, 336, 1, 1], [36, 336, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 3408, 'exponent': 252, 'exponents_of_order': [6, 3, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[14, 0, 2], [14, 1, 1], [16, 0, 2], [16, 1, 1], [42, 1, 1], [54, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 5927777241500214389, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 126, 'inner_gen_orders': [6, 18], 'inner_gens': [[1010031245, 1640591418], [1100430014, 566507649]], 'inner_hash': 246442942980519397, 'inner_nilpotent': False, 'inner_order': 6048, 'inner_split': True, 'inner_tex': 'C_2^2.\\SL(2,8).C_3', 'inner_used': [1, 2], 'irrC_degree': 14, 'irrQ_degree': 14, 'irrQ_dim': 14, 'irrR_degree': 14, 'irrep_stats': [[1, 12], [2, 3], [7, 12], [8, 12], [14, 3], [16, 3], [21, 4], [27, 4], [42, 1], [54, 1]], 'label': '12096.r', 'linC_count': 36, 'linC_degree': 9, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 4, 'linQ_dim': 9, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'D4*2G(2,3)', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 44, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 55, 'number_divisions': 40, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 231, 'number_subgroup_classes': 329, 'number_subgroups': 27698, 'old_label': None, 'order': 12096, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 383], [3, 224], [4, 128], [6, 4144], [7, 216], [9, 504], [12, 1456], [14, 1080], [18, 2520], [28, 432], [36, 1008]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [18], 'outer_gens': [[1010031263, 566507649]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 1], [7, 4], [8, 4], [14, 5], [16, 5], [21, 4], [27, 4], [28, 1], [32, 1], [42, 1], [54, 1]], 'representations': {'Perm': {'d': 13, 'gens': [1010031245, 566507649]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_4\\times {}^2G(2,3)', 'transitive_degree': 36, '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: 108592565
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 18, 'group_order': 12096, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
  • id: 108592576
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 18, 'group_order': 12096, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 16, 'size': 1}
  • id: 108592587
    {'aut_label': '2B', 'centralizer': '2.a1.a1', 'counter': 3, 'group_counter': 18, 'group_order': 12096, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 23, 'size': 2}
  • id: 108592598
    {'aut_label': '2B', 'centralizer': '2.a1.b1', 'counter': 4, 'group_counter': 18, 'group_order': 12096, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 5, 'size': 2}
  • id: 108592609
    {'aut_label': '2D', 'centralizer': '63.a1.a1', 'counter': 5, 'group_counter': 18, 'group_order': 12096, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 1038009000, 'size': 63}
  • id: 108592616
    {'aut_label': '2E', 'centralizer': '63.a1.a1', 'counter': 6, 'group_counter': 18, 'group_order': 12096, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 4134469816, 'size': 63}
  • id: 108592617
    {'aut_label': '2F', 'centralizer': '126.b1.b1', 'counter': 7, 'group_counter': 18, 'group_order': 12096, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 3879728045, 'size': 126}
  • id: 108592618
    {'aut_label': '2F', 'centralizer': '126.b1.a1', 'counter': 8, 'group_counter': 18, 'group_order': 12096, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 135732263, 'size': 126}
  • id: 108592619
    {'aut_label': '3A', 'centralizer': '56.c1.a1', 'counter': 9, 'group_counter': 18, 'group_order': 12096, 'label': '3A', 'order': 3, 'powers': [9, 1, 9], 'representative': 693630000, 'size': 56}
  • id: 108592566
    {'aut_label': '3B1', 'centralizer': '84.a1.a1', 'counter': 10, 'group_counter': 18, 'group_order': 12096, 'label': '3B1', 'order': 3, 'powers': [11, 1, 10], 'representative': 3872460360, 'size': 84}
  • id: 108592567
    {'aut_label': '3B-1', 'centralizer': '84.a1.a1', 'counter': 11, 'group_counter': 18, 'group_order': 12096, 'label': '3B-1', 'order': 3, 'powers': [10, 1, 11], 'representative': 1020153000, 'size': 84}
  • id: 108592568
    {'aut_label': '4A', 'centralizer': '2.b1.a1', 'counter': 12, 'group_counter': 18, 'group_order': 12096, 'label': '4A', 'order': 4, 'powers': [2, 12, 12], 'representative': 18, 'size': 2}
  • id: 108592569
    {'aut_label': '4B', 'centralizer': '126.e1.a1', 'counter': 13, 'group_counter': 18, 'group_order': 12096, 'label': '4B', 'order': 4, 'powers': [2, 13, 13], 'representative': 3484067769, 'size': 126}
  • id: 108592570
    {'aut_label': '6A', 'centralizer': '56.c1.a1', 'counter': 14, 'group_counter': 18, 'group_order': 12096, 'label': '6A', 'order': 6, 'powers': [9, 2, 14], 'representative': 1925094376, 'size': 56}
  • id: 108592571
    {'aut_label': '6B1', 'centralizer': '84.a1.a1', 'counter': 15, 'group_counter': 18, 'group_order': 12096, 'label': '6B1', 'order': 6, 'powers': [10, 2, 15], 'representative': 1020153016, 'size': 84}
  • id: 108592572
    {'aut_label': '6B-1', 'centralizer': '84.a1.a1', 'counter': 16, 'group_counter': 18, 'group_order': 12096, 'label': '6B-1', 'order': 6, 'powers': [11, 2, 16], 'representative': 3872460376, 'size': 84}
  • id: 108592573
    {'aut_label': '6C', 'centralizer': '112.a1.a1', 'counter': 17, 'group_counter': 18, 'group_order': 12096, 'label': '6C', 'order': 6, 'powers': [9, 3, 17], 'representative': 2882481983, 'size': 112}
  • id: 108592574
    {'aut_label': '6C', 'centralizer': '112.a1.b1', 'counter': 18, 'group_counter': 18, 'group_order': 12096, 'label': '6D', 'order': 6, 'powers': [9, 4, 18], 'representative': 3075504485, 'size': 112}
  • id: 108592575
    {'aut_label': '6E1', 'centralizer': '168.a1.b1', 'counter': 19, 'group_counter': 18, 'group_order': 12096, 'label': '6E1', 'order': 6, 'powers': [10, 4, 19], 'representative': 99843974, 'size': 168}
  • id: 108592577
    {'aut_label': '6E-1', 'centralizer': '168.a1.b1', 'counter': 20, 'group_counter': 18, 'group_order': 12096, 'label': '6E-1', 'order': 6, 'powers': [11, 4, 20], 'representative': 290476814, 'size': 168}
  • id: 108592578
    {'aut_label': '6E1', 'centralizer': '168.a1.a1', 'counter': 21, 'group_counter': 18, 'group_order': 12096, 'label': '6F1', 'order': 6, 'powers': [10, 3, 21], 'representative': 2555568127, 'size': 168}
  • id: 108592579
    {'aut_label': '6E-1', 'centralizer': '168.a1.a1', 'counter': 22, 'group_counter': 18, 'group_order': 12096, 'label': '6F-1', 'order': 6, 'powers': [11, 3, 22], 'representative': 1252702927, 'size': 168}
  • id: 108592580
    {'aut_label': '6G1', 'centralizer': '252.b1.a1', 'counter': 23, 'group_counter': 18, 'group_order': 12096, 'label': '6G1', 'order': 6, 'powers': [10, 5, 23], 'representative': 1601550840, 'size': 252}
  • id: 108592581
    {'aut_label': '6G-1', 'centralizer': '252.b1.a1', 'counter': 24, 'group_counter': 18, 'group_order': 12096, 'label': '6G-1', 'order': 6, 'powers': [11, 5, 24], 'representative': 2489518200, 'size': 252}
  • id: 108592582
    {'aut_label': '6H1', 'centralizer': '252.b1.a1', 'counter': 25, 'group_counter': 18, 'group_order': 12096, 'label': '6H1', 'order': 6, 'powers': [11, 6, 25], 'representative': 614154256, 'size': 252}
  • id: 108592583
    {'aut_label': '6H-1', 'centralizer': '252.b1.a1', 'counter': 26, 'group_counter': 18, 'group_order': 12096, 'label': '6H-1', 'order': 6, 'powers': [10, 6, 26], 'representative': 2410259176, 'size': 252}
  • id: 108592584
    {'aut_label': '6I1', 'centralizer': '504.a1.b1', 'counter': 27, 'group_counter': 18, 'group_order': 12096, 'label': '6I1', 'order': 6, 'powers': [11, 7, 27], 'representative': 1957788725, 'size': 504}
  • id: 108592585
    {'aut_label': '6I-1', 'centralizer': '504.a1.b1', 'counter': 28, 'group_counter': 18, 'group_order': 12096, 'label': '6I-1', 'order': 6, 'powers': [10, 7, 28], 'representative': 1016800685, 'size': 504}
  • id: 108592586
    {'aut_label': '6I-1', 'centralizer': '504.a1.a1', 'counter': 29, 'group_counter': 18, 'group_order': 12096, 'label': '6J1', 'order': 6, 'powers': [10, 8, 29], 'representative': 52387343, 'size': 504}
  • id: 108592588
    {'aut_label': '6I1', 'centralizer': '504.a1.a1', 'counter': 30, 'group_counter': 18, 'group_order': 12096, 'label': '6J-1', 'order': 6, 'powers': [11, 8, 30], 'representative': 281353703, 'size': 504}
  • id: 108592589
    {'aut_label': '7A', 'centralizer': '216.c1.a1', 'counter': 31, 'group_counter': 18, 'group_order': 12096, 'label': '7A', 'order': 7, 'powers': [31, 31, 1], 'representative': 3882902400, 'size': 216}
  • id: 108592590
    {'aut_label': '9A', 'centralizer': '168.f1.a1', 'counter': 32, 'group_counter': 18, 'group_order': 12096, 'label': '9A', 'order': 9, 'powers': [32, 9, 32], 'representative': 1140547800, 'size': 168}
  • id: 108592591
    {'aut_label': '9B1', 'centralizer': '168.g1.a1', 'counter': 33, 'group_counter': 18, 'group_order': 12096, 'label': '9B1', 'order': 9, 'powers': [34, 9, 33], 'representative': 1445806200, 'size': 168}
  • id: 108592592
    {'aut_label': '9B-1', 'centralizer': '168.g1.a1', 'counter': 34, 'group_counter': 18, 'group_order': 12096, 'label': '9B-1', 'order': 9, 'powers': [33, 9, 34], 'representative': 780197760, 'size': 168}
  • id: 108592593
    {'aut_label': '12A', 'centralizer': '112.d1.a1', 'counter': 35, 'group_counter': 18, 'group_order': 12096, 'label': '12A', 'order': 12, 'powers': [14, 12, 35], 'representative': 620899338, 'size': 112}
  • id: 108592594
    {'aut_label': '12B1', 'centralizer': '168.h1.a1', 'counter': 36, 'group_counter': 18, 'group_order': 12096, 'label': '12B1', 'order': 12, 'powers': [15, 12, 36], 'representative': 2014882689, 'size': 168}
  • id: 108592595
    {'aut_label': '12B-1', 'centralizer': '168.h1.a1', 'counter': 37, 'group_counter': 18, 'group_order': 12096, 'label': '12B-1', 'order': 12, 'powers': [16, 12, 37], 'representative': 4115796498, 'size': 168}
  • id: 108592596
    {'aut_label': '12C1', 'centralizer': '504.g1.a1', 'counter': 38, 'group_counter': 18, 'group_order': 12096, 'label': '12C1', 'order': 12, 'powers': [15, 13, 38], 'representative': 2533266138, 'size': 504}
  • id: 108592597
    {'aut_label': '12C-1', 'centralizer': '504.g1.a1', 'counter': 39, 'group_counter': 18, 'group_order': 12096, 'label': '12C-1', 'order': 12, 'powers': [16, 13, 39], 'representative': 2047168089, 'size': 504}
  • id: 108592599
    {'aut_label': '14A', 'centralizer': '216.c1.a1', 'counter': 40, 'group_counter': 18, 'group_order': 12096, 'label': '14A', 'order': 14, 'powers': [31, 40, 2], 'representative': 1956101056, 'size': 216}
  • id: 108592600
    {'aut_label': '14B', 'centralizer': '432.a1.a1', 'counter': 41, 'group_counter': 18, 'group_order': 12096, 'label': '14B', 'order': 14, 'powers': [31, 41, 3], 'representative': 773025967, 'size': 432}
  • id: 108592601
    {'aut_label': '14B', 'centralizer': '432.a1.b1', 'counter': 42, 'group_counter': 18, 'group_order': 12096, 'label': '14C', 'order': 14, 'powers': [31, 42, 4], 'representative': 96285005, 'size': 432}
  • id: 108592602
    {'aut_label': '18A', 'centralizer': '168.f1.a1', 'counter': 43, 'group_counter': 18, 'group_order': 12096, 'label': '18A', 'order': 18, 'powers': [32, 14, 43], 'representative': 534255856, 'size': 168}
  • id: 108592603
    {'aut_label': '18B1', 'centralizer': '168.g1.a1', 'counter': 44, 'group_counter': 18, 'group_order': 12096, 'label': '18B1', 'order': 18, 'powers': [34, 14, 44], 'representative': 3975441136, 'size': 168}
  • id: 108592604
    {'aut_label': '18B-1', 'centralizer': '168.g1.a1', 'counter': 45, 'group_counter': 18, 'group_order': 12096, 'label': '18B-1', 'order': 18, 'powers': [33, 14, 45], 'representative': 3128526136, 'size': 168}
  • id: 108592605
    {'aut_label': '18C', 'centralizer': '336.b1.a1', 'counter': 46, 'group_counter': 18, 'group_order': 12096, 'label': '18C', 'order': 18, 'powers': [32, 17, 46], 'representative': 3531307703, 'size': 336}
  • id: 108592606
    {'aut_label': '18C', 'centralizer': '336.b1.b1', 'counter': 47, 'group_counter': 18, 'group_order': 12096, 'label': '18D', 'order': 18, 'powers': [32, 18, 47], 'representative': 759282494, 'size': 336}
  • id: 108592607
    {'aut_label': '18E1', 'centralizer': '336.c1.b1', 'counter': 48, 'group_counter': 18, 'group_order': 12096, 'label': '18E1', 'order': 18, 'powers': [33, 18, 48], 'representative': 2559398525, 'size': 336}
  • id: 108592608
    {'aut_label': '18E-1', 'centralizer': '336.c1.b1', 'counter': 49, 'group_counter': 18, 'group_order': 12096, 'label': '18E-1', 'order': 18, 'powers': [34, 18, 49], 'representative': 2018741765, 'size': 336}
  • id: 108592610
    {'aut_label': '18E1', 'centralizer': '336.c1.a1', 'counter': 50, 'group_counter': 18, 'group_order': 12096, 'label': '18F1', 'order': 18, 'powers': [33, 17, 50], 'representative': 3477529567, 'size': 336}
  • id: 108592611
    {'aut_label': '18E-1', 'centralizer': '336.c1.a1', 'counter': 51, 'group_counter': 18, 'group_order': 12096, 'label': '18F-1', 'order': 18, 'powers': [34, 17, 51], 'representative': 2965259527, 'size': 336}
  • id: 108592612
    {'aut_label': '28A', 'centralizer': '432.d1.a1', 'counter': 52, 'group_counter': 18, 'group_order': 12096, 'label': '28A', 'order': 28, 'powers': [40, 52, 12], 'representative': 3409339809, 'size': 432}
  • id: 108592613
    {'aut_label': '36A', 'centralizer': '336.j1.a1', 'counter': 53, 'group_counter': 18, 'group_order': 12096, 'label': '36A', 'order': 36, 'powers': [43, 35, 53], 'representative': 2097447858, 'size': 336}
  • id: 108592614
    {'aut_label': '36B1', 'centralizer': '336.k1.a1', 'counter': 54, 'group_counter': 18, 'group_order': 12096, 'label': '36B1', 'order': 36, 'powers': [44, 35, 54], 'representative': 3553815729, 'size': 336}
  • id: 108592615
    {'aut_label': '36B-1', 'centralizer': '336.k1.a1', 'counter': 55, 'group_counter': 18, 'group_order': 12096, 'label': '36B-1', 'order': 36, 'powers': [45, 35, 55], 'representative': 1257102738, 'size': 336}
• 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: 3935246
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.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], 'schur_index': 1}
  • id: 3935257
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.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], 'schur_index': 1}
  • id: 3935268
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.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], 'schur_index': 1}
  • id: 3935279
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.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], 'schur_index': 1}
  • id: 3935281
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, 2, -1, 2, -1, -1, 2, 2, -1, -1], 'schur_index': 1}
  • id: 3935282
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.1f', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, -2, -2, 2, -1, -1, 2, 2, 2, -1, -1, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -2, -2, -1, 2, -1, 1, -2, 1, -2, 1, 1, 2, 2, -1, -1], 'schur_index': 1}
  • id: 3935283
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, 2, 2, -2, 2, -1, -1, -2, -2, 2, -1, -1, -2, 2, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 2, 2, -1, -1, -2, 1, 1, 1, 1, 2, -2, 2, -1, 2, -1, 1, 2, -1, -2, 1, -1, -2, -2, 1, 1], 'schur_index': 1}
  • id: 3935284
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, 2, -2, 2, 2, -1, -1, -2, -2, 2, -1, -1, 2, -2, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 2, 2, -1, -1, -2, 1, 1, 1, 1, 2, 2, -2, -1, 2, -1, -1, -2, 1, 2, -1, 1, -2, -2, 1, 1], 'schur_index': 1}
  • id: 3935285
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, -2, 0, 0, 2, 2, 2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, -2, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935247
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.2b', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, -4, 0, 0, 4, -2, -2, 0, 0, -4, 2, 2, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 4, 4, -2, -2, 0, 0, 0, 0, 0, -4, 0, 0, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935248
    {'cdim': 7, 'counter': 11, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.7a', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 7, 'qvalues': [7, 7, -7, -7, -1, -1, 1, 1, -2, 1, 1, 7, -1, -2, 1, 1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, 1, 1, 1, -2, 1, 1, -1, -1, 0, 0, 0, 1, 1, 1, -1, -1, -1, -1, -1, -1, 0, 1, 1, 1], 'schur_index': 1}
  • id: 3935249
    {'cdim': 7, 'counter': 12, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.7b', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 7, 'qvalues': [7, 7, -7, 7, -1, -1, -1, 1, -2, 1, 1, -7, 1, -2, 1, 1, 2, -2, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 0, 1, 1, 1, 2, -1, -1, 1, 1, 0, 0, 0, 1, 1, 1, -1, 1, 1, -1, -1, 1, 0, -1, -1, -1], 'schur_index': 1}
  • id: 3935250
    {'cdim': 7, 'counter': 13, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.7c', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 7, 'qvalues': [7, 7, 7, -7, -1, -1, 1, -1, -2, 1, 1, -7, 1, -2, 1, 1, -2, 2, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 0, 1, 1, 1, 2, -1, -1, 1, 1, 0, 0, 0, 1, 1, 1, 1, -1, -1, 1, 1, -1, 0, -1, -1, -1], 'schur_index': 1}
  • id: 3935251
    {'cdim': 7, 'counter': 14, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.7d', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 7, 'qvalues': [7, 7, 7, 7, -1, -1, -1, -1, -2, 1, 1, 7, -1, -2, 1, 1, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 1, 1, 1, -2, 1, 1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1], 'schur_index': 1}
  • id: 3935256
    {'cdim': 8, 'counter': 19, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.8a', 'multiplicity': 1, 'nt': [9, 32], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, -1, 2, 2, 8, 0, -1, 2, 2, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 2, 2, 0, 0, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3935258
    {'cdim': 8, 'counter': 20, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.8b', 'multiplicity': 1, 'nt': [18, 427], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, -1, 2, 2, 8, 0, -1, 2, 2, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 2, 2, 0, 0, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 3935259
    {'cdim': 8, 'counter': 21, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.8c', 'multiplicity': 1, 'nt': [18, 427], 'qdim': 8, 'qvalues': [8, 8, -8, 8, 0, 0, 0, 0, -1, 2, 2, -8, 0, -1, 2, 2, 1, -1, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, 1, -2, -2, 0, 0, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 3935260
    {'cdim': 8, 'counter': 22, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.8d', 'multiplicity': 1, 'nt': [18, 427], 'qdim': 8, 'qvalues': [8, 8, 8, -8, 0, 0, 0, 0, -1, 2, 2, -8, 0, -1, 2, 2, -1, 1, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, 1, -2, -2, 0, 0, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 3935252
    {'cdim': 7, 'counter': 15, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.7e', 'multiplicity': 2, 'nt': [168, 0], 'qdim': 14, 'qvalues': [14, 14, -14, -14, -2, -2, 2, 2, -4, -1, -1, 14, -2, -4, -1, -1, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 2, -1, -1, -4, -1, -1, 1, 1, 0, 0, 0, -1, 2, -1, 1, -2, 1, -2, 1, 1, 0, 2, -1, -1], 'schur_index': 1}
  • id: 3935253
    {'cdim': 7, 'counter': 16, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.7f', 'multiplicity': 2, 'nt': [168, 0], 'qdim': 14, 'qvalues': [14, 14, -14, 14, -2, -2, -2, 2, -4, -1, -1, -14, 2, -4, -1, -1, 4, -4, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 0, 2, -1, -1, 4, 1, 1, -1, -1, 0, 0, 0, -1, 2, -1, 1, 2, -1, -2, 1, -1, 0, -2, 1, 1], 'schur_index': 1}
  • id: 3935254
    {'cdim': 7, 'counter': 17, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.7g', 'multiplicity': 2, 'nt': [168, 0], 'qdim': 14, 'qvalues': [14, 14, 14, -14, -2, -2, 2, -2, -4, -1, -1, -14, 2, -4, -1, -1, -4, 4, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 0, 2, -1, -1, 4, 1, 1, -1, -1, 0, 0, 0, -1, 2, -1, -1, -2, 1, 2, -1, 1, 0, -2, 1, 1], 'schur_index': 1}
  • id: 3935255
    {'cdim': 7, 'counter': 18, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.7h', 'multiplicity': 2, 'nt': [168, 0], 'qdim': 14, 'qvalues': [14, 14, 14, 14, -2, -2, -2, -2, -4, -1, -1, 14, -2, -4, -1, -1, -4, -4, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, -1, -1, -4, -1, -1, 1, 1, 0, 0, 0, -1, 2, -1, -1, 2, -1, 2, -1, -1, 0, 2, -1, -1], 'schur_index': 1}
  • id: 3935265
    {'cdim': 14, 'counter': 27, 'faithful': True, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.14a', 'multiplicity': 1, 'nt': [112, 0], 'qdim': 14, 'qvalues': [14, -14, 0, 0, -2, 2, 0, 0, -4, 2, 2, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935261
    {'cdim': 8, 'counter': 23, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.8e', 'multiplicity': 2, 'nt': [27, 391], 'qdim': 16, 'qvalues': [16, 16, 16, 16, 0, 0, 0, 0, -2, -2, -2, 16, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, 1, -2, -2, -2, 0, 0, 2, 2, 2, 1, -2, 1, 1, -2, 1, -2, 1, 1, 2, -2, 1, 1], 'schur_index': 1}
  • id: 3935262
    {'cdim': 8, 'counter': 24, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.8f', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 0, 0, 0, 0, -2, -2, -2, 16, 0, -2, -2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, 1, -2, -2, -2, 0, 0, 2, -2, -2, 1, -2, 1, -1, 2, -1, 2, -1, -1, 2, -2, 1, 1], 'schur_index': 1}
  • id: 3935263
    {'cdim': 8, 'counter': 25, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.8g', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 16, 'qvalues': [16, 16, -16, 16, 0, 0, 0, 0, -2, -2, -2, -16, 0, -2, -2, -2, 2, -2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, 1, 2, 2, 2, 0, 0, 2, -2, 2, 1, -2, 1, -1, -2, 1, 2, -1, 1, -2, 2, -1, -1], 'schur_index': 1}
  • id: 3935264
    {'cdim': 8, 'counter': 26, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.8h', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 16, 'qvalues': [16, 16, 16, -16, 0, 0, 0, 0, -2, -2, -2, -16, 0, -2, -2, -2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 1, 1, 2, 2, 2, 0, 0, 2, 2, -2, 1, -2, 1, 1, 2, -1, -2, 1, -1, -2, 2, -1, -1], 'schur_index': 1}
  • id: 3935267
    {'cdim': 16, 'counter': 29, 'faithful': True, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.16a', 'multiplicity': 1, 'nt': [36, 9588], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, -2, 4, 4, 0, 0, 2, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935270
    {'cdim': 21, 'counter': 31, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.21a', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 21, 'qvalues': [21, 21, -21, -21, -3, -3, 3, 3, 3, 0, 0, 21, -3, 3, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935271
    {'cdim': 21, 'counter': 32, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.21b', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 21, 'qvalues': [21, 21, -21, 21, -3, -3, -3, 3, 3, 0, 0, -21, 3, 3, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935272
    {'cdim': 21, 'counter': 33, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.21c', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 21, 'qvalues': [21, 21, 21, -21, -3, -3, 3, -3, 3, 0, 0, -21, 3, 3, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935273
    {'cdim': 21, 'counter': 34, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.21d', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 21, 'qvalues': [21, 21, 21, 21, -3, -3, -3, -3, 3, 0, 0, 21, -3, 3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935274
    {'cdim': 27, 'counter': 35, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.27a', 'multiplicity': 1, 'nt': [28, 165], 'qdim': 27, 'qvalues': [27, 27, 27, 27, 3, 3, 3, 3, 0, 0, 0, 27, 3, 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, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], 'schur_index': 1}
  • id: 3935275
    {'cdim': 27, 'counter': 36, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.27b', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 27, 'qvalues': [27, 27, -27, -27, 3, 3, -3, -3, 0, 0, 0, 27, 3, 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, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], 'schur_index': 1}
  • id: 3935276
    {'cdim': 27, 'counter': 37, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.27c', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 27, 'qvalues': [27, 27, -27, 27, 3, 3, 3, -3, 0, 0, 0, -27, -3, 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, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], 'schur_index': 1}
  • id: 3935277
    {'cdim': 27, 'counter': 38, 'faithful': False, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.27d', 'multiplicity': 1, 'nt': [56, 0], 'qdim': 27, 'qvalues': [27, 27, 27, -27, 3, 3, -3, 3, 0, 0, 0, -27, -3, 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, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], 'schur_index': 1}
  • id: 3935266
    {'cdim': 14, 'counter': 28, 'faithful': True, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.14b', 'multiplicity': 2, 'nt': [336, 0], 'qdim': 28, 'qvalues': [28, -28, 0, 0, -4, 4, 0, 0, -8, -2, -2, 0, 0, 8, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935269
    {'cdim': 16, 'counter': 30, 'faithful': True, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.16b', 'multiplicity': 2, 'nt': [108, 0], 'qdim': 32, 'qvalues': [32, -32, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 2, 2, 0, 0, 0, 0, 0, -4, 0, 0, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935278
    {'cdim': 42, 'counter': 39, 'faithful': True, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.42a', 'multiplicity': 1, 'nt': [112, 0], 'qdim': 42, 'qvalues': [42, -42, 0, 0, -6, 6, 0, 0, 6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 3935280
    {'cdim': 54, 'counter': 40, 'faithful': True, 'group': '12096.r', 'group_order': 12096, 'image': None, 'label': '12096.r.54a', 'multiplicity': 1, 'nt': [112, 0], 'qdim': 54, 'qvalues': [54, -54, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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: 5500262
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 12096, 'label': '12096.r.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]]]}
  • id: 5500273
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 6048, 'label': '12096.r.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]]]}
  • id: 5500284
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 6048, 'label': '12096.r.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]]]}
  • id: 5500295
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 6048, 'label': '12096.r.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]]]}
  • id: 5500306
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 4032, 'label': '12096.r.1e1', 'nt': [3, 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, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 5500313
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 4032, 'label': '12096.r.1e2', 'nt': [3, 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, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 5500314
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 2016, 'label': '12096.r.1f1', 'nt': [6, 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, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 5500315
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 2016, 'label': '12096.r.1f2', 'nt': [6, 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, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 5500316
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 2016, 'label': '12096.r.1g1', 'nt': [6, 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, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 5500263
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.b1', 'kernel_order': 2016, 'label': '12096.r.1g2', 'nt': [6, 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, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 5500264
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 2016, 'label': '12096.r.1h1', 'nt': [6, 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, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 5500265
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 12096, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 2016, 'label': '12096.r.1h2', 'nt': [6, 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, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 5500266
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 3024, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1.a1', 'kernel_order': 1512, 'label': '12096.r.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 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]]]}
  • id: 5500267
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 3024, 'counter': 14, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 504, 'label': '12096.r.2b1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500268
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 3024, 'counter': 15, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1.a1', 'kernel_order': 504, 'label': '12096.r.2b2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500269
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 16, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.b1.a1', 'kernel_order': 4, 'label': '12096.r.7a', 'nt': [56, 0], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5500270
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 17, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.a1.b1', 'kernel_order': 4, 'label': '12096.r.7b', 'nt': [56, 0], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-7, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5500271
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 18, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.a1.a1', 'kernel_order': 4, 'label': '12096.r.7c', 'nt': [56, 0], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-7, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5500272
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '1512.779', 'image_order': 1512, 'indicator': 1, 'kernel': '1512.a1.a1', 'kernel_order': 8, 'label': '12096.r.7d', 'nt': [56, 0], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[7, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5500274
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 20, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.b1.a1', 'kernel_order': 4, 'label': '12096.r.7e1', 'nt': [168, 0], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[7, 0]], [[-1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[2, 0]], [[2, 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]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 5500275
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 21, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.b1.a1', 'kernel_order': 4, 'label': '12096.r.7e2', 'nt': [168, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[7, 0]], [[-1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[2, 0]], [[2, 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]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 5500276
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 22, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.a1.b1', 'kernel_order': 4, 'label': '12096.r.7f1', 'nt': [168, 0], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-7, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[2, 0]], [[-2, 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]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 5500277
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 23, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.a1.b1', 'kernel_order': 4, 'label': '12096.r.7f2', 'nt': [168, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-7, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[2, 0]], [[-2, 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]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 5500278
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 24, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.a1.a1', 'kernel_order': 4, 'label': '12096.r.7g1', 'nt': [168, 0], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-7, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, 0]], [[2, 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]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 5500279
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 25, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.a1.a1', 'kernel_order': 4, 'label': '12096.r.7g2', 'nt': [168, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-7, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 0]], [[2, 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]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 5500280
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 26, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '1512.779', 'image_order': 1512, 'indicator': 0, 'kernel': '1512.a1.a1', 'kernel_order': 8, 'label': '12096.r.7h1', 'nt': [168, 0], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[7, 0]], [[-1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 5500281
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 27, 'cyclotomic_n': 3, 'dim': 7, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '1512.779', 'image_order': 1512, 'indicator': 0, 'kernel': '1512.a1.a1', 'kernel_order': 8, 'label': '12096.r.7h2', 'nt': [168, 2], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[7, 0]], [[-1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 5500282
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 28, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '1512.779', 'image_order': 1512, 'indicator': 1, 'kernel': '1512.a1.a1', 'kernel_order': 8, 'label': '12096.r.8a', 'nt': [9, 32], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[8, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5500283
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.b1.a1', 'kernel_order': 4, 'label': '12096.r.8b', 'nt': [18, 427], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[8, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 5500285
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 30, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.a1.b1', 'kernel_order': 4, 'label': '12096.r.8c', 'nt': [18, 427], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-8, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5500286
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 31, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.a1.a1', 'kernel_order': 4, 'label': '12096.r.8d', 'nt': [18, 427], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-8, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 5500287
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 32, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '1512.779', 'image_order': 1512, 'indicator': 0, 'kernel': '1512.a1.a1', 'kernel_order': 8, 'label': '12096.r.8e1', 'nt': [27, 391], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[8, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 5500288
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 33, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '1512.779', 'image_order': 1512, 'indicator': 0, 'kernel': '1512.a1.a1', 'kernel_order': 8, 'label': '12096.r.8e2', 'nt': [27, 2], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[8, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 5500289
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.b1.a1', 'kernel_order': 4, 'label': '12096.r.8f1', 'nt': [54, 0], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[8, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[1, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 5500290
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 35, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.b1.a1', 'kernel_order': 4, 'label': '12096.r.8f2', 'nt': [54, 2], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[8, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[1, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 5500291
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 36, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.a1.b1', 'kernel_order': 4, 'label': '12096.r.8g1', 'nt': [54, 0], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-8, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[1, 0]], [[-1, 0]], [[2, 1]], [[-2, -1]], [[2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 5500292
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 37, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.a1.b1', 'kernel_order': 4, 'label': '12096.r.8g2', 'nt': [54, 2], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-8, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[1, 0]], [[-1, 0]], [[2, -1]], [[-2, 1]], [[2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 5500293
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 38, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.a1.a1', 'kernel_order': 4, 'label': '12096.r.8h1', 'nt': [54, 0], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-8, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[1, 0]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 5500294
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 39, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 0, 'kernel': '3024.a1.a1', 'kernel_order': 4, 'label': '12096.r.8h2', 'nt': [54, 2], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-8, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[1, 0]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 5500296
    {'center': '6048.a1.a1', 'center_index': 6048, 'center_order': 2, 'counter': 40, 'cyclotomic_n': 1, 'dim': 14, 'faithful': True, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '12096.r', 'image_order': 12096, 'indicator': 1, 'kernel': '12096.a1.a1', 'kernel_order': 1, 'label': '12096.r.14a', 'nt': [112, 0], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
  • id: 5500297
    {'center': '6048.a1.a1', 'center_index': 6048, 'center_order': 2, 'counter': 41, 'cyclotomic_n': 3, 'dim': 14, 'faithful': True, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '12096.r', 'image_order': 12096, 'indicator': 0, 'kernel': '12096.a1.a1', 'kernel_order': 1, 'label': '12096.r.14b1', 'nt': [336, 0], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500298
    {'center': '6048.a1.a1', 'center_index': 6048, 'center_order': 2, 'counter': 42, 'cyclotomic_n': 3, 'dim': 14, 'faithful': True, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '12096.r', 'image_order': 12096, 'indicator': 0, 'kernel': '12096.a1.a1', 'kernel_order': 1, 'label': '12096.r.14b2', 'nt': [336, 2], 'q_character': None, 'values': [[[14, 0]], [[-14, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500299
    {'center': '6048.a1.a1', 'center_index': 6048, 'center_order': 2, 'counter': 43, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '12096.r', 'image_order': 12096, 'indicator': 1, 'kernel': '12096.a1.a1', 'kernel_order': 1, 'label': '12096.r.16a', 'nt': [36, 9588], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 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]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 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]]]}
  • id: 5500300
    {'center': '6048.a1.a1', 'center_index': 6048, 'center_order': 2, 'counter': 44, 'cyclotomic_n': 3, 'dim': 16, 'faithful': True, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '12096.r', 'image_order': 12096, 'indicator': 0, 'kernel': '12096.a1.a1', 'kernel_order': 1, 'label': '12096.r.16b1', 'nt': [108, 0], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500301
    {'center': '6048.a1.a1', 'center_index': 6048, 'center_order': 2, 'counter': 45, 'cyclotomic_n': 3, 'dim': 16, 'faithful': True, 'field': [1, -1, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '12096.r', 'image_order': 12096, 'indicator': 0, 'kernel': '12096.a1.a1', 'kernel_order': 1, 'label': '12096.r.16b2', 'nt': [108, 2], 'q_character': None, 'values': [[[16, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500302
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 46, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.b1.a1', 'kernel_order': 4, 'label': '12096.r.21a', 'nt': [56, 0], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[-21, 0]], [[-21, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[21, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500303
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 47, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.a1.b1', 'kernel_order': 4, 'label': '12096.r.21b', 'nt': [56, 0], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[-21, 0]], [[21, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-21, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500304
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 48, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.a1.a1', 'kernel_order': 4, 'label': '12096.r.21c', 'nt': [56, 0], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[21, 0]], [[-21, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-21, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500305
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 49, 'cyclotomic_n': 1, 'dim': 21, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '1512.779', 'image_order': 1512, 'indicator': 1, 'kernel': '1512.a1.a1', 'kernel_order': 8, 'label': '12096.r.21d', 'nt': [56, 0], 'q_character': None, 'values': [[[21, 0]], [[21, 0]], [[21, 0]], [[21, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[21, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500307
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 50, 'cyclotomic_n': 1, 'dim': 27, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '1512.779', 'image_order': 1512, 'indicator': 1, 'kernel': '1512.a1.a1', 'kernel_order': 8, 'label': '12096.r.27a', 'nt': [28, 165], 'q_character': None, 'values': [[[27, 0]], [[27, 0]], [[27, 0]], [[27, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[27, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500308
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 51, 'cyclotomic_n': 1, 'dim': 27, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.b1.a1', 'kernel_order': 4, 'label': '12096.r.27b', 'nt': [56, 0], 'q_character': None, 'values': [[[27, 0]], [[27, 0]], [[-27, 0]], [[-27, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[27, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500309
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 52, 'cyclotomic_n': 1, 'dim': 27, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.a1.b1', 'kernel_order': 4, 'label': '12096.r.27c', 'nt': [56, 0], 'q_character': None, 'values': [[[27, 0]], [[27, 0]], [[-27, 0]], [[27, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-27, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500310
    {'center': '1512.a1.a1', 'center_index': 1512, 'center_order': 8, 'counter': 53, 'cyclotomic_n': 1, 'dim': 27, 'faithful': False, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': None, 'image_order': 3024, 'indicator': 1, 'kernel': '3024.a1.a1', 'kernel_order': 4, 'label': '12096.r.27d', 'nt': [56, 0], 'q_character': None, 'values': [[[27, 0]], [[27, 0]], [[27, 0]], [[-27, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-27, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 5500311
    {'center': '6048.a1.a1', 'center_index': 6048, 'center_order': 2, 'counter': 54, 'cyclotomic_n': 1, 'dim': 42, 'faithful': True, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '12096.r', 'image_order': 12096, 'indicator': 1, 'kernel': '12096.a1.a1', 'kernel_order': 1, 'label': '12096.r.42a', 'nt': [112, 0], 'q_character': None, 'values': [[[42, 0]], [[-42, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 5500312
    {'center': '6048.a1.a1', 'center_index': 6048, 'center_order': 2, 'counter': 55, 'cyclotomic_n': 1, 'dim': 54, 'faithful': True, 'field': [0, 1], 'group': '12096.r', 'group_counter': 18, 'group_order': 12096, 'image': None, 'image_isoclass': '12096.r', 'image_order': 12096, 'indicator': 1, 'kernel': '12096.a1.a1', 'kernel_order': 1, 'label': '12096.r.54a', 'nt': [112, 0], 'q_character': None, 'values': [[[54, 0]], [[-54, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]]]}
• 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: 61380973
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 12096, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '12096.r.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': False, 'special_labels': ['L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12096.r', 'subgroup_hash': 5927777241500214389, 'subgroup_order': 12096, 'subgroup_tex': 'D_4\\times {}^2G(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 61381084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6048, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 246442942980519397, 'subgroup_order': 6048, 'subgroup_tex': 'C_2^2.\\SL(2,8).C_3', 'supersolvable': False, 'sylow': 0}
  • id: 61381195
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6048, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 246442942980519397, 'subgroup_order': 6048, 'subgroup_tex': 'C_2^2.\\SL(2,8).C_3', 'supersolvable': False, 'sylow': 0}
  • id: 61381236
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 6048, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6258485434785906295, 'subgroup_order': 6048, 'subgroup_tex': 'C_4.\\SL(2,8).C_3', 'supersolvable': False, 'sylow': 0}
  • id: 61381247
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 4032, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.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': False, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5146313423022937384, 'subgroup_order': 4032, 'subgroup_tex': 'D_4.\\SL(2,8)', 'supersolvable': False, 'sylow': 0}
  • id: 61381258
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 3024, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.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': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5679810977767407995, 'subgroup_order': 3024, 'subgroup_tex': 'C_2.\\SL(2,8).C_3', 'supersolvable': False, 'sylow': 0}
  • id: 61381269
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1512, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5679810977767407995, 'subgroup_order': 3024, 'subgroup_tex': 'C_2.\\SL(2,8).C_3', 'supersolvable': False, 'sylow': 0}
  • id: 61381280
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1512, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5679810977767407995, 'subgroup_order': 3024, 'subgroup_tex': 'C_2.\\SL(2,8).C_3', 'supersolvable': False, 'sylow': 0}
  • id: 61381291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2016, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.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': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5317091110057418036, 'subgroup_order': 2016, 'subgroup_tex': 'C_2^2.\\SL(2,8)', 'supersolvable': False, 'sylow': 0}
  • id: 61380974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2016, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.b1', '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': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5317091110057418036, 'subgroup_order': 2016, 'subgroup_tex': 'C_2^2.\\SL(2,8)', 'supersolvable': False, 'sylow': 0}
  • id: 61380985
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 2016, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1630473112464293879, 'subgroup_order': 2016, 'subgroup_tex': 'C_4.\\SL(2,8)', 'supersolvable': False, 'sylow': 0}
  • id: 61380996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 1512, 'counter': 12, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '12096.r.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1512.779', 'subgroup_hash': 779, 'subgroup_order': 1512, 'subgroup_tex': '{}^2G(2,3)', 'supersolvable': False, 'sylow': 0}
  • id: 61381007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, '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': '1344.11307', 'subgroup_hash': 11307, 'subgroup_order': 1344, 'subgroup_tex': 'D_4\\times F_8:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 61381018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 1008, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.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': '12.5', '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': False, 'special_labels': ['D', 'S', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1008.880', 'subgroup_hash': 880, 'subgroup_order': 1008, 'subgroup_tex': 'C_2\\times \\SL(2,8)', 'supersolvable': False, 'sylow': 0}
  • id: 61381029
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 504, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1008.880', 'subgroup_hash': 880, 'subgroup_order': 1008, 'subgroup_tex': 'C_2\\times \\SL(2,8)', 'supersolvable': False, 'sylow': 0}
  • id: 61381040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 504, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1008.880', 'subgroup_hash': 880, 'subgroup_order': 1008, 'subgroup_tex': 'C_2\\times \\SL(2,8)', 'supersolvable': False, 'sylow': 0}
  • id: 61381051
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1256', 'subgroup_hash': 1256, 'subgroup_order': 672, 'subgroup_tex': 'C_2\\times F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 61381062
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1256', 'subgroup_hash': 1256, 'subgroup_order': 672, 'subgroup_tex': 'C_2\\times F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 61381073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '672.1049', 'subgroup_hash': 1049, 'subgroup_order': 672, 'subgroup_tex': 'F_8:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 61381085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 504, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': True, 'solvable': False, 'special_labels': ['PC', 'L2', 'D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '504.156', 'subgroup_hash': 156, 'subgroup_order': 504, 'subgroup_tex': '\\SL(2,8)', 'supersolvable': False, 'sylow': 0}
  • id: 61381096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '12096.r.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '448.1363', 'subgroup_hash': 1363, 'subgroup_order': 448, 'subgroup_tex': 'D_4\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 61381107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.28.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.362', 'subgroup_hash': 362, 'subgroup_order': 432, 'subgroup_tex': 'D_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.36.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.125', 'subgroup_hash': 125, 'subgroup_order': 336, 'subgroup_tex': 'D_4\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381129
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.210', 'subgroup_hash': 210, 'subgroup_order': 336, 'subgroup_tex': 'F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 61381140
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.210', 'subgroup_hash': 210, 'subgroup_order': 336, 'subgroup_tex': 'F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 61381151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '336.210', 'subgroup_hash': 210, 'subgroup_order': 336, 'subgroup_tex': 'F_8:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 61381162
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.195', 'subgroup_hash': 195, 'subgroup_order': 224, 'subgroup_tex': 'C_2^2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 61381173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.54.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.195', 'subgroup_hash': 195, 'subgroup_order': 224, 'subgroup_tex': 'C_2^2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 61381184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.173', 'subgroup_hash': 173, 'subgroup_order': 224, 'subgroup_tex': 'C_4\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 61381196
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.56.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.111', 'subgroup_hash': 111, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.56.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.111', 'subgroup_hash': 111, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.56.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.62', 'subgroup_hash': 62, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381229
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.56.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.62', 'subgroup_hash': 62, 'subgroup_order': 216, 'subgroup_tex': 'D_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381230
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.56.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.78', 'subgroup_hash': 78, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.56.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.53', 'subgroup_hash': 53, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381232
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.56.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.54', 'subgroup_hash': 54, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.63.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '63.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': 63, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1497', 'subgroup_hash': 1497, 'subgroup_order': 192, 'subgroup_tex': 'C_2^5:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 61381234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.47', 'subgroup_hash': 47, 'subgroup_order': 168, 'subgroup_tex': 'C_2^2\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.72.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.47', 'subgroup_hash': 47, 'subgroup_order': 168, 'subgroup_tex': 'C_2^2\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381237
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.11', 'subgroup_hash': 11, 'subgroup_order': 168, 'subgroup_tex': 'D_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381238
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.72.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.11', 'subgroup_hash': 11, 'subgroup_order': 168, 'subgroup_tex': 'D_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381239
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.20', 'subgroup_hash': 20, 'subgroup_order': 168, 'subgroup_tex': 'C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.8', 'subgroup_hash': 8, 'subgroup_order': 168, 'subgroup_tex': 'C_4\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381241
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.9', 'subgroup_hash': 9, 'subgroup_order': 168, 'subgroup_tex': 'C_{28}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '168.43', 'subgroup_hash': 43, 'subgroup_order': 168, 'subgroup_tex': 'F_8:C_3', 'supersolvable': False, 'sylow': 0}
  • id: 61381243
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.84.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.84.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '84.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': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.41', 'subgroup_hash': 41, 'subgroup_order': 144, 'subgroup_tex': 'D_4\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381245
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.31', 'subgroup_hash': 31, 'subgroup_order': 112, 'subgroup_tex': 'D_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.41', 'subgroup_hash': 41, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 61381248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.41', 'subgroup_hash': 41, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 61381249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.108.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.41', 'subgroup_hash': 41, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 61381250
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381251
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381252
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381254
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.14', 'subgroup_hash': 14, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61381256
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61381257
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381259
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381260
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381261
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.112.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381262
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.126.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.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': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381263
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.126.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381264
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.126.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.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': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381265
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.126.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.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': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.228', 'subgroup_hash': 228, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.126.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.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': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.126.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.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': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.197', 'subgroup_hash': 197, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.126.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '126.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': 126, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.196', 'subgroup_hash': 196, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 61381270
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381271
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.9', 'subgroup_hash': 9, 'subgroup_order': 84, 'subgroup_tex': 'C_{14}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.7', 'subgroup_hash': 7, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.7', 'subgroup_hash': 7, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.7', 'subgroup_hash': 7, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381275
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.2', 'subgroup_hash': 2, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61381276
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.1', 'subgroup_hash': 1, 'subgroup_order': 84, 'subgroup_tex': 'C_7:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61381277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.7', 'subgroup_hash': 7, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381278
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.7', 'subgroup_hash': 7, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.7', 'subgroup_hash': 7, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.144.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.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': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '84.7', 'subgroup_hash': 7, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381282
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381283
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.17', 'subgroup_hash': 17, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.17', 'subgroup_hash': 17, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61381287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61381288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.8', 'subgroup_hash': 8, 'subgroup_order': 72, 'subgroup_tex': 'C_9:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.8', 'subgroup_hash': 8, 'subgroup_order': 72, 'subgroup_tex': 'C_9:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 61381292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 8, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.10', 'subgroup_hash': 10, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, '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: 61381295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.5', 'subgroup_hash': 5, 'subgroup_order': 72, 'subgroup_tex': 'C_4\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61381297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.168.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.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': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.6', 'subgroup_hash': 6, 'subgroup_order': 72, 'subgroup_tex': 'D_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 61381298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '12096.r.189.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '189.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': 189, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.261', 'subgroup_hash': 261, 'subgroup_order': 64, 'subgroup_tex': 'D_4\\times C_2^3', 'supersolvable': True, 'sylow': 2}
  • id: 61381299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381300
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.216.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.12', 'subgroup_hash': 12, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61380975
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.216.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.7', 'subgroup_hash': 7, 'subgroup_order': 56, 'subgroup_tex': 'C_7:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61380976
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 8, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.9', 'subgroup_hash': 9, 'subgroup_order': 56, 'subgroup_tex': 'C_7\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61380977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.4', 'subgroup_hash': 4, 'subgroup_order': 56, 'subgroup_tex': 'C_4\\times D_7', 'supersolvable': True, 'sylow': 0}
  • id: 61380978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.5', 'subgroup_hash': 5, 'subgroup_order': 56, 'subgroup_tex': 'D_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 61380979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.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': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.11', 'subgroup_hash': 11, 'subgroup_order': 56, 'subgroup_tex': 'F_8', 'supersolvable': False, 'sylow': 0}
  • id: 61380980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61380981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.224.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61380982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.224.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61380983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.224.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61380984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.224.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61380986
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.224.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61380987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.224.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61380988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61380989
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61380990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61380991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61380992
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61380993
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61380994
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61380995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61380997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61380998
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61380999
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.252.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '252.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': 252, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.49', 'subgroup_hash': 49, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381002
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381003
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.288.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381004
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.288.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.2', 'subgroup_hash': 2, 'subgroup_order': 42, 'subgroup_tex': 'C_7:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381005
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381006
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.288.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381008
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.288.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381009
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.288.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.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': 288, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '42.1', 'subgroup_hash': 1, 'subgroup_order': 42, 'subgroup_tex': 'F_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381010
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 61381011
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 61381012
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381014
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381015
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381016
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': 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: 61381017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381019
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': 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: 61381020
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': 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: 61381021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': 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: 61381024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': 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: 61381025
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.336.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 61381026
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.336.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.2', 'subgroup_hash': 2, 'subgroup_order': 36, 'subgroup_tex': 'C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 61381027
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.1', 'subgroup_hash': 1, 'subgroup_order': 36, 'subgroup_tex': 'C_9:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': 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: 61381030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': 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: 61381031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': 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: 61381034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': 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: 61381035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.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': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.336.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '336.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.378.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '378.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': 378, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381038
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.378.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '378.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 378, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381039
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.378.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '378.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': 378, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 61381041
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.378.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '378.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': 378, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 61381042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.378.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '378.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': 378, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.378.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '378.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': 378, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381044
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.378.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '378.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': 378, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381045
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381046
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381050
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 4, 'counter': 169, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.432.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
  • id: 61381052
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.1', 'subgroup_hash': 1, 'subgroup_order': 28, 'subgroup_tex': 'C_7:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381053
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.432.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '432.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': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.3', 'subgroup_hash': 3, 'subgroup_order': 28, 'subgroup_tex': 'D_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '12096.r.448.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.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': 448, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 3}
  • id: 61381058
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381059
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '504.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 61381063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381066
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 8, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381069
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, '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: 61381070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, '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: 61381071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381074
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 61381075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381080
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.504.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '504.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': 504, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381081
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '576.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': 576, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '21.1', 'subgroup_hash': 1, 'subgroup_order': 21, 'subgroup_tex': 'C_7:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 61381082
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': 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: 61381083
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 199, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.672.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381086
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.672.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381087
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': 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: 61381088
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': 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: 61381089
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.672.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381090
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.672.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381091
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.672.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381092
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.672.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 61381093
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': 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: 61381094
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381095
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': 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: 61381097
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381098
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': 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: 61381099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': 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: 61381100
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381101
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.672.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '672.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': 672, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381104
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61381105
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61381106
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.e1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.e1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381111
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61381112
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61381113
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381114
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381115
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61381116
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61381117
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61381119
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61381120
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.756.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '756.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': 756, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 61381121
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 2, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.864.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381122
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.864.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.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': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381123
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 28, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.864.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.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': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 61381124
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.864.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.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': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381125
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.864.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.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': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381126
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.864.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.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': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381127
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.864.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '864.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': 864, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.1', 'subgroup_hash': 1, 'subgroup_order': 14, 'subgroup_tex': 'D_7', 'supersolvable': True, 'sylow': 0}
  • id: 61381128
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381130
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1008, 'quotient_simple': 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: 61381131
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381132
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381133
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381135
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381139
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 249, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.1008.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381141
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381142
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 251, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.1008.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381143
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 252, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.1008.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381144
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381145
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381146
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381148
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381149
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': 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: 61381153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1008.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1008.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': 1008, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 61381154
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1344.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1344.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': 1344, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 61381155
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.1344.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1344.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': 1344, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381156
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.1344.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1344.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': 1344, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 61381157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': True, 'centralizer_order': 3024, 'characteristic': True, 'core_order': 8, 'counter': 265, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '12096.r.1512.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1512.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1512.779', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 779, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1512, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '{}^2G(2,3)', 'simple': False, 'solvable': True, 'special_labels': ['F', 'R', 'U0', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381158
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381159
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381161
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381163
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381164
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381165
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381166
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381167
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381168
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381169
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381170
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.i1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381171
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381172
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381174
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381175
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381176
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381177
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381178
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381179
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381181
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.1512.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1512.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': 1512, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 61381182
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 56, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '12096.r.1728.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1728.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': 1728, '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': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 61381183
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 289, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381185
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 290, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381186
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381187
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381188
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381189
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381190
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381191
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.2016.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381192
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 297, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381193
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.2016.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381194
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381197
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.2016.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381198
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.2016.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381199
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.2016.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '2016.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': 2016, 'quotient_simple': 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: 61381200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6048, 'characteristic': False, 'core_order': 4, 'counter': 303, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.3024.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3024.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5679810977767407995, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 3024, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2.\\SL(2,8).C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61381201
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6048, 'characteristic': False, 'core_order': 4, 'counter': 304, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12096.r.3024.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3024.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5679810977767407995, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 3024, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2.\\SL(2,8).C_3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 61381202
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6048, 'characteristic': True, 'core_order': 4, 'counter': 305, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '12096.r.3024.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3024.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5679810977767407995, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 3024, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2.\\SL(2,8).C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 61381203
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 2, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381204
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381205
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381206
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 309, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.3024.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381208
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381209
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381210
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381211
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381212
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381213
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381214
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381215
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381216
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381217
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '12096.r.3024.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3024.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': 3024, 'quotient_simple': 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: 61381219
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 320, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.4032.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4032.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': 4032, '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: 61381220
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 321, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.4032.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4032.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': 4032, '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: 61381221
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': True, 'central_factor': False, 'centralizer_order': 12096, 'characteristic': True, 'core_order': 2, 'counter': 322, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '12096.r.6048.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '6048.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 246442942980519397, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6048, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2.\\SL(2,8).C_3', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1', 'C4'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 61381222
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6048, 'characteristic': False, 'core_order': 1, 'counter': 323, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.6048.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6048.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': 6048, '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: 61381223
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 6048, 'characteristic': False, 'core_order': 1, 'counter': 324, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.6048.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6048.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': 6048, '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: 61381224
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 325, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.6048.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6048.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': 6048, '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: 61381225
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 192, 'characteristic': False, 'core_order': 1, 'counter': 326, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.6048.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6048.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': 6048, '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: 61381226
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 327, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.6048.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6048.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': 6048, '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: 61381227
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 1, 'counter': 328, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '12096.r.6048.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6048.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': 6048, '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: 61381228
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '12096.r', 'ambient_counter': 18, 'ambient_order': 12096, 'ambient_tex': 'D_4\\times {}^2G(2,3)', 'central': True, 'central_factor': False, 'centralizer_order': 12096, 'characteristic': True, 'core_order': 1, 'counter': 329, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '12096.r.12096.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12096.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '12096.r', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5927777241500214389, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12096, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'D_4\\times {}^2G(2,3)', 'simple': False, 'solvable': True, 'special_labels': ['U2', 'C5'], '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: 61381029
    {'ambient': '12096.r', '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': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '108.c1.a1', '336.n1.a1', '432.f1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1356, -1, 4183, -1, 1465, -1, 1195, -1], 'generators': [2977159687, 3017352967, 7], 'label': '12096.r.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1512.779'}
  • id: 61380991
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['84.a1.a1', '84.b1.a1'], 'contains': ['504.b1.a1', '504.b1.b1', '504.d1.a1', '504.d1.b1', '504.e1.a1', '504.h1.a1', '504.k1.a1', '756.c1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [5052, -1, 3495, -1, 7470, -1, 7448, -1], 'generators': [2087786169, 5, 16, 2933254814, 9], 'label': '12096.r.252.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '252.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61380973
    {'ambient': '12096.r', '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': '6048.a1.a1', 'complements': ['12096.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '3.a1.a1', '9.a1.a1', '28.a1.a1', '36.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7888, 3652, 5885, 3913, 3684, 4931, 3592, 4983], 'generators': [1097123049, 2203575127, 5, 16, 9], 'label': '12096.r.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '10000.dk', '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': '10000.dk'}
  • id: 61380974
    {'ambient': '12096.r', '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': '3024.a1.b1', 'complements': ['2016.d1.a1', '2016.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.b1', '54.a1.b1', '168.b1.b1', '216.a1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2877, 1806, 5624, 1177, 2540, 7597, 1918, 8214], 'generators': [3017352965, 5, 16, 2977159685], 'label': '12096.r.6.a1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.b1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '3024.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 61380975
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.b1', '108.a1.a1'], 'contains': ['432.a1.b1', '432.c1.b1', '432.e1.a1', '1512.c1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9721, -1, 7359, -1, 3658, -1, 3530, -1], 'generators': [1099567560, 999821658, 5, 16], 'label': '12096.r.216.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.b1', 'subgroup_fusion': None, 'weyl_group': '168.47'}
  • id: 61380976
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '72.c1.a1', '108.a1.a1'], 'contains': ['432.a1.a1', '432.a1.b1', '432.d1.a1', '1512.a1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8717, -1, 7848, -1, 4344, -1, 3911, -1], 'generators': [2453431687, 5, 16, 9], 'label': '12096.r.216.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.15'}
  • id: 61380977
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '72.d1.a1', '108.a1.a1'], 'contains': ['432.b1.a1', '432.d1.a1', '432.e1.a1', '1512.e1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8880, -1, 6503, -1, 3862, -1, 4025, -1], 'generators': [1099567578, 999821658, 16, 9], 'label': '12096.r.216.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61380978
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '108.a1.a1'], 'contains': ['432.c1.a1', '432.c1.b1', '432.d1.a1', '1512.h1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9957, -1, 6646, -1, 4205, -1, 3617, -1], 'generators': [1099567578, 999821647, 16, 9], 'label': '12096.r.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '168.47'}
  • id: 61380979
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '72.f1.a1', '108.b1.a1', '108.c1.a1', '108.c1.b1'], 'contains': ['1512.o1.a1', '1728.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1374, -1, 4654, -1, 33, -1, 23, -1], 'generators': [3129567840, 1574910000, 3604255920, 2453431680], 'label': '12096.r.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.f1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 61380980
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '112.a1.b1', '112.b1.a1', '112.c1.a1', '112.c1.b1', '112.d1.a1', '112.e1.a1'], 'contains': ['448.a1.a1', '672.a1.a1', '672.b1.a1', '672.c1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2922, -1, 868, -1, 9446, -1, 9228, -1], 'generators': [3844124776, 763233976, 16, 1681587360], 'label': '12096.r.224.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '224.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 61380981
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '224.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '112.f1.a1', '112.g1.a1'], 'contains': ['448.a1.a1', '672.d1.a1', '672.e1.a1', '672.f1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [575, -1, 600, -1, 8820, -1, 8877, -1], 'generators': [3844124760, 7, 763233967, 1681587360], 'label': '12096.r.224.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '224.b1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 61380982
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '224.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.b1', '112.f1.b1', '112.g1.b1'], 'contains': ['448.a1.a1', '672.d1.b1', '672.e1.b1', '672.f1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [575, -1, 2142, -1, 8820, -1, 8359, -1], 'generators': [763233965, 5, 3844124765, 1681587360], 'label': '12096.r.224.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '224.b1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 61380983
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '224.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '112.b1.a1', '112.f1.a1', '112.f1.b1'], 'contains': ['448.a1.a1', '672.g1.a1', '672.h1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [346, -1, 3315, -1, 8107, -1, 8098, -1], 'generators': [3844124760, 1604388960, 763233960, 1681587360], 'label': '12096.r.224.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '224.c1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61380984
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1.a1', '112.g1.a1', '112.g1.b1'], 'contains': ['448.a1.a1', '672.i1.a1', '672.j1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1173, -1, 2517, -1, 8219, -1, 8468, -1], 'generators': [1604388976, 3844124760, 763233960, 1681587360], 'label': '12096.r.224.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '224.d1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61380985
    {'ambient': '12096.r', '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': '3024.b1.a1', 'complements': ['2016.i1.b1', '2016.i1.a1', '2016.d1.a1', '2016.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '54.b1.a1', '168.i1.a1', '216.d1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7662, 5548, 5992, 6576, 3637, 4590, 4264, 3646], 'generators': [2977159689, 3017352969, 16, 9], 'label': '12096.r.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '3024.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 61380986
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.a1', '112.f1.b1', '112.g1.b1'], 'contains': ['448.a1.a1', '672.k1.a1', '672.l1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [749, -1, 2410, -1, 8442, -1, 8175, -1], 'generators': [3844124760, 1604388974, 763233960, 1681587360], 'label': '12096.r.224.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '224.e1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61380987
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.b1', '112.f1.a1', '112.g1.a1'], 'contains': ['448.a1.a1', '672.k1.b1', '672.l1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [749, -1, 1066, -1, 8442, -1, 8545, -1], 'generators': [1604388967, 3844124760, 763233960, 1681587360], 'label': '12096.r.224.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '224.e1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61380988
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.a1.a1', '126.b1.a1', '126.c1.a1'], 'contains': ['504.i1.a1', '504.l1.a1', '756.b1.a1', '1008.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6861, -1, 9309, -1, 2123, -1, 3218, -1], 'generators': [2202727103, 1727355720, 7, 16, 1158358447], 'label': '12096.r.252.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '252.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61380989
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.a1.b1', '126.b1.b1', '126.c1.a1'], 'contains': ['504.i1.a1', '504.l1.b1', '756.b1.b1', '1008.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 63, 'diagramx': [6861, -1, 8672, -1, 2123, -1, 2437, -1], 'generators': [1158358454, 1727355725, 5, 16, 2202727085], 'label': '12096.r.252.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '252.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61380990
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '63.a1.a1', '84.a1.a1'], 'contains': ['504.a1.a1', '504.a1.b1', '504.c1.a1', '504.c1.b1', '504.f1.a1', '504.g1.a1', '504.j1.a1', '756.c1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [8524, -1, 8029, -1, 5438, -1, 5426, -1], 'generators': [3974076847, 2202727103, 5, 16, 9], 'label': '12096.r.252.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '252.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61380992
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.a1.a1', '126.b1.b1', '126.d1.a1'], 'contains': ['504.i1.a1', '504.n1.a1', '756.f1.a1', '1008.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7136, -1, 8496, -1, 1885, -1, 2306, -1], 'generators': [3974076854, 1158358440, 1727355720, 16, 2202727096], 'label': '12096.r.252.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '252.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61380993
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.a1.b1', '126.b1.a1', '126.d1.a1'], 'contains': ['504.i1.a1', '504.n1.b1', '756.f1.b1', '1008.e1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7136, -1, 8379, -1, 1885, -1, 2568, -1], 'generators': [3974076847, 1158358440, 1727355720, 16, 2202727096], 'label': '12096.r.252.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '252.d1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61380994
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.c1.a1', '126.d1.a1', '126.e1.a1'], 'contains': ['504.i1.a1', '756.g1.a1', '1008.i1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [8074, -1, 9142, -1, 4948, -1, 4848, -1], 'generators': [2202727089, 1727355720, 16, 1158358458, 9], 'label': '12096.r.252.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '252.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61380995
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.a1.a1', '126.a1.b1', '126.e1.a1'], 'contains': ['504.i1.a1', '756.h1.a1', '1008.j1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7446, -1, 8869, -1, 3296, -1, 4735, -1], 'generators': [1158358440, 1727355720, 16, 3974076858, 2202727096], 'label': '12096.r.252.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '252.f1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61380996
    {'ambient': '12096.r', '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': '1512.a1.a1', 'complements': ['1512.c1.b1', '1512.i1.a1', '1512.i1.a2', '1512.c1.a1', '1512.h1.a1', '1512.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['24.a1.a1', '72.f1.a1', '224.c1.a1', '288.c1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1240, 8995, 4519, 8823, 644, 1924, 711, 2455], 'generators': [2203575120, 1097123040], 'label': '12096.r.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '12096.r', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1512.779'}
  • id: 61380997
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '126.b1.a1', '126.b1.b1', '126.e1.a1'], 'contains': ['504.i1.a1', '504.m1.a1', '504.o1.a1', '756.i1.a1', '1008.c1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6495, -1, 6774, -1, 1218, -1, 1631, -1], 'generators': [1158358440, 1727355720, 3974076840, 16, 2202727096], 'label': '12096.r.252.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '252.g1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61380998
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.b1.a1'], 'contains': ['504.l1.a1', '504.m1.a1', '504.n1.b1', '756.j1.a1', '1008.m1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [6154, -1, 5996, -1, 1409, -1, 1793, -1], 'generators': [3974076847, 23, 2202727103, 1158358463, 1727355720], 'label': '12096.r.252.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '252.h1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61380999
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.b1.b1'], 'contains': ['504.l1.b1', '504.m1.a1', '504.n1.a1', '756.j1.b1', '1008.m1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [6154, -1, 7548, -1, 1409, -1, 1127, -1], 'generators': [3974076854, 1727355725, 5, 1158358445, 2202727085], 'label': '12096.r.252.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '252.h1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381000
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '126.b1.a1'], 'contains': ['504.l1.a1', '504.n1.b1', '504.o1.a1', '756.k1.a1', '1008.k1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4154, -1, 5251, -1, 760, -1, 1469, -1], 'generators': [3974076847, 2202727087, 1727355720, 7, 1158358447], 'label': '12096.r.252.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '252.i1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381001
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '252.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '126.b1.b1'], 'contains': ['504.l1.b1', '504.n1.a1', '504.o1.a1', '756.k1.b1', '1008.k1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4154, -1, 6286, -1, 760, -1, 607, -1], 'generators': [3974076854, 1158358454, 14, 1727355734, 2202727094], 'label': '12096.r.252.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '252.i1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '252.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381002
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '144.a1.a1', '144.a1.b1', '144.b1.a1', '144.c1.a1', '144.c1.b1', '144.d1.a1', '144.e1.a1'], 'contains': ['576.a1.a1', '864.a1.a1', '2016.b1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9460, -1, 7155, -1, 2881, -1, 2813, -1], 'generators': [1442090280, 16, 2202727096], 'label': '12096.r.288.a1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381003
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '144.a1.a1', '144.f1.a1', '144.g1.a1'], 'contains': ['576.a1.a1', '864.b1.a1', '2016.d1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2515, -1, 4539, -1, 1808, -1, 2008, -1], 'generators': [2202727087, 1442090280, 7], 'label': '12096.r.288.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '288.b1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381004
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.b1', '144.a1.b1', '144.f1.b1', '144.g1.b1'], 'contains': ['576.a1.a1', '864.b1.b1', '2016.d1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2515, -1, 5457, -1, 1808, -1, 728, -1], 'generators': [1442090280, 5, 2202727085], 'label': '12096.r.288.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.b1', 'old_label': '288.b1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381005
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '144.b1.a1', '144.f1.a1', '144.f1.b1'], 'contains': ['576.a1.a1', '864.c1.a1', '2016.e1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1942, -1, 4420, -1, 1259, -1, 896, -1], 'generators': [204791760, 125319720, 1038009000], 'label': '12096.r.288.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '288.c1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381006
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.g1.a1', '144.g1.b1'], 'contains': ['576.a1.a1', '864.d1.a1', '2016.g1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5566, -1, 4984, -1, 2042, -1, 1390, -1], 'generators': [204791760, 125319720, 1038009016], 'label': '12096.r.288.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '288.d1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381007
    {'ambient': '12096.r', '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': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['18.a1.a1', '18.a1.b1', '18.b1.a1', '27.a1.a1', '63.a1.a1', '72.c1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8219, -1, 6972, -1, 3215, -1, 3592, -1], 'generators': [3974076847, 2202727103, 1442090280, 1727355725, 5, 16, 1158358447, 9], 'label': '12096.r.9.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '10000.dk', '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': '672.1256'}
  • id: 61381008
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '144.f1.b1', '144.g1.b1'], 'contains': ['576.a1.a1', '864.e1.a1', '2016.i1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5320, -1, 5633, -1, 1954, -1, 1032, -1], 'generators': [204791760, 125319720, 1038009005], 'label': '12096.r.288.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.b1', 'old_label': '288.e1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381009
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.b1', '144.f1.a1', '144.g1.a1'], 'contains': ['576.a1.a1', '864.e1.b1', '2016.i1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5320, -1, 4751, -1, 1954, -1, 1519, -1], 'generators': [204791760, 125319720, 1038009007], 'label': '12096.r.288.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '288.e1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381010
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '168.a1.a1', '168.c1.a1', '168.e1.a1'], 'contains': ['672.a1.a1', '672.d1.a1', '1008.a1.a1', '1008.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3276, -1, 944, -1, 6848, -1, 7055, -1], 'generators': [3844124776, 7, 16, 763233983], 'label': '12096.r.336.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381011
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.b1', '168.a1.b1', '168.c1.b1', '168.e1.a1'], 'contains': ['672.a1.a1', '672.d1.b1', '1008.a1.b1', '1008.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [3276, -1, 650, -1, 6848, -1, 6742, -1], 'generators': [763233965, 3844124774, 5, 16], 'label': '12096.r.336.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381012
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '168.b1.a1', '168.d1.a1', '168.f1.a1'], 'contains': ['672.b1.a1', '672.e1.a1', '1008.a1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2969, -1, 1591, -1, 9130, -1, 9654, -1], 'generators': [696851407, 2087786183, 7, 16], 'label': '12096.r.336.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381013
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.b1', '168.b1.b1', '168.d1.b1', '168.f1.a1'], 'contains': ['672.b1.a1', '672.e1.b1', '1008.a1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [2969, -1, 1468, -1, 9130, -1, 9090, -1], 'generators': [696851414, 2087786176, 5, 16], 'label': '12096.r.336.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381014
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.a1', '168.g1.a1'], 'contains': ['672.c1.a1', '672.f1.a1', '1008.a1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3468, -1, 177, -1, 9756, -1, 9865, -1], 'generators': [3844124776, 7, 16, 1681587360], 'label': '12096.r.336.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.c1.a1', 'old_label': '336.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381015
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1.b1', '168.g1.a1'], 'contains': ['672.c1.a1', '672.f1.b1', '1008.a1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 56, 'diagramx': [3468, -1, 54, -1, 9756, -1, 9366, -1], 'generators': [3844124774, 5, 16, 1681587360], 'label': '12096.r.336.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.c1.a1', 'old_label': '336.c1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.c1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381016
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1.a1', '168.a1.a1', '168.a1.b1', '168.h1.a1'], 'contains': ['672.a1.a1', '672.g1.a1', '672.i1.a1', '1008.c1.a1', '1008.d1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2258, -1, 3615, -1, 6166, -1, 6424, -1], 'generators': [3844124776, 1604388960, 763233976, 16], 'label': '12096.r.336.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '336.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381017
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '112.b1.a1', '168.b1.a1', '168.b1.b1', '168.i1.a1'], 'contains': ['672.b1.a1', '672.h1.a1', '672.j1.a1', '1008.d1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1768, -1, 3998, -1, 8554, -1, 8695, -1], 'generators': [696851400, 2087786176, 16, 2933254816], 'label': '12096.r.336.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.e1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381018
    {'ambient': '12096.r', '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': '1512.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.b1.a1'], 'contains': ['24.a1.a1', '108.b1.a1', '336.e1.a1', '432.b1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3087, 5548, 5341, 6321, 2398, 4590, 1691, 4475], 'generators': [2977159696, 3017352976, 16], 'label': '12096.r.12.a1.a1', 'mobius_quo': 1, 'mobius_sub': -2, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.a1.b1', '6.b1.a1'], 'normal_contains': ['24.a1.a1', '6048.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1512.779'}
  • id: 61381019
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.a1', '168.a1.b1', '168.c1.a1', '168.j1.a1'], 'contains': ['672.a1.a1', '672.k1.a1', '1008.e1.a1', '1008.f1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3146, -1, 2322, -1, 6715, -1, 6538, -1], 'generators': [3844124776, 1604388974, 763233976, 16], 'label': '12096.r.336.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '336.f1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381020
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.b1', '168.a1.a1', '168.c1.b1', '168.j1.a1'], 'contains': ['672.a1.a1', '672.k1.b1', '1008.e1.b1', '1008.f1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3146, -1, 862, -1, 6715, -1, 6964, -1], 'generators': [3844124776, 1604388967, 763233976, 16], 'label': '12096.r.336.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '336.f1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.f1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381021
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.a1', '168.b1.b1', '168.d1.a1', '168.k1.a1'], 'contains': ['672.b1.a1', '672.l1.a1', '1008.f1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2682, -1, 2851, -1, 8976, -1, 8770, -1], 'generators': [696851400, 2087786176, 16, 2933254814], 'label': '12096.r.336.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.g1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381022
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.c1.b1', '168.b1.a1', '168.d1.b1', '168.k1.a1'], 'contains': ['672.b1.a1', '672.l1.b1', '1008.f1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2682, -1, 2436, -1, 8976, -1, 9471, -1], 'generators': [696851400, 2087786176, 2933254823, 16], 'label': '12096.r.336.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.g1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.g1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381023
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d1.a1', '168.e1.a1', '168.h1.a1', '168.j1.a1'], 'contains': ['672.a1.a1', '1008.g1.a1', '1008.i1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4661, -1, 1316, -1, 7508, -1, 7328, -1], 'generators': [3844124776, 16, 763233969, 9], 'label': '12096.r.336.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.h1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381024
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.e1.a1', '168.c1.a1', '168.c1.b1', '168.h1.a1'], 'contains': ['672.a1.a1', '1008.h1.a1', '1008.j1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [5128, -1, 1066, -1, 7192, -1, 7190, -1], 'generators': [3844124776, 1604388978, 763233976, 16], 'label': '12096.r.336.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '336.i1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381025
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d1.a1', '168.f1.a1', '168.i1.a1', '168.k1.a1'], 'contains': ['672.b1.a1', '1008.g1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3753, -1, 1929, -1, 9602, -1, 9760, -1], 'generators': [696851418, 2087786169, 16, 9], 'label': '12096.r.336.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.j1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381026
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.d1.a1', '168.g1.a1'], 'contains': ['672.c1.a1', '1008.g1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3903, -1, 357, -1, 9910, -1, 9970, -1], 'generators': [3844124776, 16, 1681587360, 9], 'label': '12096.r.336.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.c1.a1', 'old_label': '336.k1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381027
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.e1.a1', '168.d1.a1', '168.d1.b1', '168.i1.a1'], 'contains': ['672.b1.a1', '1008.h1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4372, -1, 2150, -1, 9287, -1, 9547, -1], 'generators': [696851400, 2087786176, 2933254818, 16], 'label': '12096.r.336.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '336.l1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.l1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381028
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.f1.a1', '168.a1.a1'], 'contains': ['672.d1.a1', '672.g1.a1', '672.k1.b1', '1008.k1.a1', '1008.l1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1069, -1, 1703, -1, 5836, -1, 6312, -1], 'generators': [1604388967, 3844124760, 7, 763233967], 'label': '12096.r.336.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '336.m1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381030
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.f1.b1', '168.a1.b1'], 'contains': ['672.d1.b1', '672.g1.a1', '672.k1.a1', '1008.k1.b1', '1008.l1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1069, -1, 3122, -1, 5836, -1, 6086, -1], 'generators': [1604388960, 14, 3844124774, 763233974], 'label': '12096.r.336.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.b1', 'old_label': '336.m1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381031
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '112.f1.a1', '168.b1.a1'], 'contains': ['672.e1.a1', '672.h1.a1', '672.l1.b1', '1008.l1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [43, -1, 3321, -1, 8331, -1, 8621, -1], 'generators': [23, 696851423, 2087786183, 2933254800], 'label': '12096.r.336.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '336.n1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.n1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381032
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '112.f1.b1', '168.b1.b1'], 'contains': ['672.e1.b1', '672.h1.a1', '672.l1.a1', '1008.l1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [43, -1, 3700, -1, 8331, -1, 8022, -1], 'generators': [2087786160, 696851405, 5, 2933254805], 'label': '12096.r.336.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '336.n1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.n1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381033
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.g1.a1', '168.a1.a1'], 'contains': ['672.d1.a1', '672.i1.a1', '672.k1.b1', '1008.m1.a1', '1008.n1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1354, -1, 731, -1, 6001, -1, 6651, -1], 'generators': [3844124760, 1604388983, 7, 763233967], 'label': '12096.r.336.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '336.o1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381034
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.g1.b1', '168.a1.b1'], 'contains': ['672.d1.b1', '672.i1.a1', '672.k1.a1', '1008.m1.b1', '1008.n1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1354, -1, 2766, -1, 6001, -1, 6199, -1], 'generators': [1604388976, 14, 3844124774, 763233974], 'label': '12096.r.336.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.b1', 'old_label': '336.o1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381035
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.g1.a1', '168.b1.a1'], 'contains': ['672.e1.a1', '672.j1.a1', '672.l1.b1', '1008.n1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [728, -1, 2025, -1, 8663, -1, 8984, -1], 'generators': [23, 696851423, 2087786183, 2933254816], 'label': '12096.r.336.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '336.p1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.p1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381036
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '336.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.g1.b1', '168.b1.b1'], 'contains': ['672.e1.b1', '672.j1.a1', '672.l1.a1', '1008.n1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [728, -1, 3003, -1, 8663, -1, 8251, -1], 'generators': [2087786160, 696851405, 5, 2933254814], 'label': '12096.r.336.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '336.p1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.p1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381037
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '378.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.a1.a1', '189.a1.a1'], 'contains': ['756.a1.a1', '756.b1.a1', '756.e1.a1', '756.e1.a2', '756.f1.a1', '756.h1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7363, -1, 9702, -1, 2923, -1, 4448, -1], 'generators': [3604255925, 1574910005, 7, 16, 3129567863], 'label': '12096.r.378.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '378.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '378.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381038
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '378.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.a1.b1', '189.a1.a1'], 'contains': ['756.a1.b1', '756.b1.b1', '756.e1.a1', '756.e1.a2', '756.f1.b1', '756.h1.a1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 63, 'diagramx': [7363, -1, 9289, -1, 2923, -1, 4316, -1], 'generators': [3604255925, 1574910005, 5, 16, 3129567863], 'label': '12096.r.378.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '378.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '378.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381039
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '378.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '126.b1.a1', '189.a1.a1'], 'contains': ['756.b1.a1', '756.f1.b1', '756.i1.a1', '756.j1.a1', '756.k1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6677, -1, 6404, -1, 1072, -1, 2030, -1], 'generators': [1574910000, 3604255920, 7, 16, 3129567863], 'label': '12096.r.378.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '378.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '378.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 61381040
    {'ambient': '12096.r', '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': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.b1'], 'contains': ['24.a1.a1', '108.c1.b1', '336.n1.b1', '432.f1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1356, -1, 4843, -1, 1465, -1, 566, -1], 'generators': [3017352965, 5, 2977159685], 'label': '12096.r.12.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '12.b1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1512.779'}
  • id: 61381041
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '378.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.b1', '126.b1.b1', '189.a1.a1'], 'contains': ['756.b1.b1', '756.f1.a1', '756.i1.a1', '756.j1.b1', '756.k1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6677, -1, 7545, -1, 1072, -1, 1369, -1], 'generators': [3604255925, 1574910005, 5, 16, 3129567845], 'label': '12096.r.378.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '378.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '378.b1.b1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 61381042
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '378.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.c1.a1', '189.a1.a1'], 'contains': ['756.a1.a1', '756.a1.b1', '756.b1.a1', '756.b1.b1', '756.c1.a1', '756.d1.a1', '756.g1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7830, -1, 9489, -1, 4722, -1, 5003, -1], 'generators': [3604255925, 1574910005, 5, 16, 9], 'label': '12096.r.378.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '378.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '378.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381043
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '378.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['126.d1.a1', '189.a1.a1'], 'contains': ['756.d1.a1', '756.e1.a1', '756.e1.a2', '756.f1.a1', '756.f1.b1', '756.g1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [8018, -1, 9139, -1, 4528, -1, 4580, -1], 'generators': [3604255925, 1574910005, 16, 3129567863, 9], 'label': '12096.r.378.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '378.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '378.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381044
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '378.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '126.e1.a1', '189.a1.a1'], 'contains': ['756.g1.a1', '756.h1.a1', '756.i1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7641, -1, 8791, -1, 3117, -1, 4184, -1], 'generators': [1574910000, 3604255920, 16, 3129567849, 9], 'label': '12096.r.378.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '378.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '378.e1.a1', 'subgroup_fusion': None, 'weyl_group': '42.2'}
  • id: 61381045
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '144.a1.a1', '216.a1.a1', '216.b1.a1', '216.c1.a1'], 'contains': ['864.a1.a1', '864.b1.a1', '3024.a1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9027, -1, 5827, -1, 3083, -1, 3237, -1], 'generators': [2453431687, 7, 16], 'label': '12096.r.432.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381046
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.b1', '144.a1.b1', '216.a1.b1', '216.b1.b1', '216.c1.a1'], 'contains': ['864.a1.a1', '864.b1.b1', '3024.a1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9027, -1, 7081, -1, 3083, -1, 2675, -1], 'generators': [2453431694, 5, 16], 'label': '12096.r.432.a1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '432.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381047
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '144.b1.a1', '216.a1.a1', '216.a1.b1', '216.d1.a1'], 'contains': ['864.a1.a1', '864.c1.a1', '864.d1.a1', '3024.c1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5740, -1, 5578, -1, 2724, -1, 2569, -1], 'generators': [1099567560, 999821640, 16], 'label': '12096.r.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '432.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381048
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '216.a1.b1', '216.b1.a1', '216.e1.a1'], 'contains': ['864.a1.a1', '864.e1.a1', '3024.d1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9898, -1, 6744, -1, 3237, -1, 3057, -1], 'generators': [1099567560, 999821654, 16], 'label': '12096.r.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '432.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381049
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.b1', '216.a1.a1', '216.b1.b1', '216.e1.a1'], 'contains': ['864.a1.a1', '864.e1.b1', '3024.d1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9898, -1, 6619, -1, 3237, -1, 3132, -1], 'generators': [1099567560, 999821647, 16], 'label': '12096.r.432.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '432.c1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.b1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381050
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '144.d1.a1', '216.c1.a1', '216.d1.a1', '216.e1.a1'], 'contains': ['864.a1.a1', '3024.b1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9309, -1, 7718, -1, 4159, -1, 4258, -1], 'generators': [2453431698, 16, 9], 'label': '12096.r.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '432.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381051
    {'ambient': '12096.r', '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': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '54.a1.a1', '126.b1.a1', '144.a1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6777, -1, 5597, -1, 1885, -1, 2291, -1], 'generators': [3974076847, 2202727103, 1727355720, 1442090280, 7, 16, 1158358447], 'label': '12096.r.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 61381052
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '216.b1.a1', '216.b1.b1', '216.d1.a1'], 'contains': ['864.a1.a1', '3024.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9659, -1, 6985, -1, 4049, -1, 4183, -1], 'generators': [1099567560, 999821658, 16], 'label': '12096.r.432.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '432.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381053
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '144.f1.a1', '216.a1.a1'], 'contains': ['864.b1.a1', '864.c1.a1', '864.e1.b1', '3024.f1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2198, -1, 4206, -1, 1358, -1, 1901, -1], 'generators': [999821647, 1099567567, 7], 'label': '12096.r.432.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '432.f1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381054
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '144.f1.b1', '216.a1.b1'], 'contains': ['864.b1.b1', '864.c1.a1', '864.e1.a1', '3024.f1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2198, -1, 4854, -1, 1358, -1, 347, -1], 'generators': [1099567560, 999821640, 5], 'label': '12096.r.432.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.b1', 'old_label': '432.f1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381055
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1.a1', '216.a1.a1'], 'contains': ['864.b1.a1', '864.d1.a1', '864.e1.b1', '3024.g1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5137, -1, 4519, -1, 2141, -1, 2116, -1], 'generators': [999821663, 1099567567, 7], 'label': '12096.r.432.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '432.g1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381056
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1.b1', '216.a1.b1'], 'contains': ['864.b1.b1', '864.d1.a1', '864.e1.a1', '3024.g1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5137, -1, 5674, -1, 2141, -1, 964, -1], 'generators': [1099567560, 999821656, 5], 'label': '12096.r.432.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.b1', 'old_label': '432.g1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381057
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '448.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.a1.a1', '224.b1.a1', '224.b1.b1', '224.c1.a1', '224.d1.a1', '224.e1.a1', '224.e1.b1'], 'contains': ['1344.a1.a1', '1344.b1.a1', '1344.c1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [462, -1, 1499, -1, 8380, -1, 8379, -1], 'generators': [3844124760, 763233960, 1681587360], 'label': '12096.r.448.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '448.a1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 61381058
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '126.b1.a1', '168.a1.a1', '252.b1.a1'], 'contains': ['1008.b1.a1', '1008.c1.a1', '1008.e1.b1', '1008.k1.a1', '1008.m1.a1', '1512.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [6444, -1, 5962, -1, 3296, -1, 4451, -1], 'generators': [3974076847, 2202727103, 7, 16], 'label': '12096.r.504.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '504.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381059
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.b1', '126.b1.b1', '168.a1.b1', '252.b1.a1'], 'contains': ['1008.b1.b1', '1008.c1.a1', '1008.e1.a1', '1008.k1.b1', '1008.m1.b1', '1512.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 252, 'diagramx': [6444, -1, 7202, -1, 3296, -1, 3318, -1], 'generators': [3974076854, 5, 16, 2202727085], 'label': '12096.r.504.a1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '504.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381060
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.a1.a1', '168.b1.a1', '252.c1.a1'], 'contains': ['1008.a1.a1', '1008.d1.a1', '1008.f1.b1', '1008.l1.a1', '1008.n1.a1', '1512.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2283, -1, 3637, -1, 6994, -1, 7463, -1], 'generators': [2087786183, 7, 16, 2933254816], 'label': '12096.r.504.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '504.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381061
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.a1.b1', '168.b1.b1', '252.c1.a1'], 'contains': ['1008.a1.b1', '1008.d1.a1', '1008.f1.a1', '1008.l1.b1', '1008.n1.b1', '1512.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [2283, -1, 3754, -1, 6994, -1, 6841, -1], 'generators': [2087786176, 5, 16, 2933254814], 'label': '12096.r.504.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '504.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381062
    {'ambient': '12096.r', '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': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.c1.b1', '54.a1.b1', '126.b1.b1', '144.a1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6777, -1, 6726, -1, 1885, -1, 1545, -1], 'generators': [3974076854, 1158358454, 1442090280, 1727355725, 5, 16, 2202727085], 'label': '12096.r.18.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 61381063
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '126.a1.a1', '168.c1.a1', '252.b1.a1'], 'contains': ['1008.b1.a1', '1008.e1.a1', '1008.j1.a1', '1512.c1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [8533, -1, 7830, -1, 5087, -1, 5656, -1], 'generators': [2202727103, 7, 16, 3974076858], 'label': '12096.r.504.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '504.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381064
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.b1', '126.a1.b1', '168.c1.b1', '252.b1.a1'], 'contains': ['1008.b1.b1', '1008.e1.b1', '1008.j1.a1', '1512.c1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 252, 'diagramx': [8533, -1, 8152, -1, 5087, -1, 5312, -1], 'generators': [3974076847, 5, 16, 2202727085], 'label': '12096.r.504.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '504.c1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381065
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.c1.a1', '168.d1.a1', '252.c1.a1'], 'contains': ['1008.a1.a1', '1008.f1.a1', '1008.h1.a1', '1512.c1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3859, -1, 2437, -1, 7352, -1, 7719, -1], 'generators': [2087786183, 7, 16, 2933254814], 'label': '12096.r.504.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '504.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61381066
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.c1.b1', '168.d1.b1', '252.c1.a1'], 'contains': ['1008.a1.b1', '1008.f1.b1', '1008.h1.a1', '1512.c1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [3859, -1, 1844, -1, 7352, -1, 7566, -1], 'generators': [2087786176, 2933254823, 5, 16], 'label': '12096.r.504.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '504.d1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61381122
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '288.b1.a1', '432.a1.a1', '432.f1.a1', '432.g1.a1'], 'contains': ['1728.a1.a1', '6048.b1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2540, -1, 4419, -1, 1911, -1, 2477, -1], 'generators': [2453431687, 7], 'label': '12096.r.864.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '864.b1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381067
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '224.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.e1.a1', '168.f1.a1', '168.g1.a1', '252.c1.a1'], 'contains': ['1008.a1.a1', '1008.a1.b1', '1008.g1.a1', '1512.a1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4491, -1, 381, -1, 7966, -1, 7928, -1], 'generators': [2087786169, 5, 16, 9], 'label': '12096.r.504.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '504.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 61381068
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '126.c1.a1', '168.e1.a1', '252.b1.a1'], 'contains': ['1008.b1.a1', '1008.b1.b1', '1008.i1.a1', '1512.a1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [8370, -1, 8435, -1, 6548, -1, 5972, -1], 'generators': [2202727103, 5, 16, 9], 'label': '12096.r.504.f1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '504.f1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381069
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '126.e1.a1', '168.h1.a1', '252.b1.a1'], 'contains': ['1008.c1.a1', '1008.i1.a1', '1008.j1.a1', '1512.e1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [8758, -1, 8321, -1, 5438, -1, 5814, -1], 'generators': [2202727089, 16, 3974076858, 9], 'label': '12096.r.504.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '504.g1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381070
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.h1.a1', '168.i1.a1', '252.c1.a1'], 'contains': ['1008.d1.a1', '1008.g1.a1', '1008.h1.a1', '1512.e1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [5468, -1, 3922, -1, 7691, -1, 7814, -1], 'generators': [2087786169, 16, 2933254816, 9], 'label': '12096.r.504.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '504.h1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381071
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.a1.a1', '252.a1.b1', '252.d1.a1', '252.d1.b1', '252.e1.a1', '252.f1.a1', '252.g1.a1'], 'contains': ['1008.o1.a1', '1512.g1.a1', '2016.b1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6981, -1, 8795, -1, 1365, -1, 2346, -1], 'generators': [1158358440, 1727355720, 16, 2202727096], 'label': '12096.r.504.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '504.i1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381072
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '126.d1.a1', '168.j1.a1', '252.b1.a1'], 'contains': ['1008.e1.a1', '1008.e1.b1', '1008.i1.a1', '1512.h1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [8936, -1, 8019, -1, 6381, -1, 5426, -1], 'generators': [2202727089, 3974076847, 16, 9], 'label': '12096.r.504.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '504.j1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381073
    {'ambient': '12096.r', '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': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '54.b1.a1', '126.e1.a1', '144.d1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8055, -1, 7667, -1, 2931, -1, 3896, -1], 'generators': [2202727089, 1727355720, 1442090280, 16, 3974076858, 1158358458, 9], 'label': '12096.r.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '10000.dk', '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': '336.210'}
  • id: 61381074
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['168.j1.a1', '168.k1.a1', '252.c1.a1'], 'contains': ['1008.f1.a1', '1008.f1.b1', '1008.g1.a1', '1512.h1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4265, -1, 3304, -1, 7828, -1, 7642, -1], 'generators': [2087786169, 16, 2933254814, 9], 'label': '12096.r.504.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '504.k1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61381075
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.a1.a1', '252.h1.a1', '252.i1.a1'], 'contains': ['1008.o1.a1', '1512.k1.a1', '2016.d1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5720, -1, 6173, -1, 1005, -1, 1564, -1], 'generators': [2202727087, 1727355720, 7, 1158358447], 'label': '12096.r.504.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '504.l1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381076
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.a1.b1', '252.h1.b1', '252.i1.b1'], 'contains': ['1008.o1.a1', '1512.k1.b1', '2016.d1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5720, -1, 7006, -1, 1005, -1, 664, -1], 'generators': [1727355725, 5, 1158358445, 2202727085], 'label': '12096.r.504.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '504.l1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.l1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381077
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.g1.a1', '252.h1.a1', '252.h1.b1'], 'contains': ['1008.o1.a1', '1512.m1.a1', '2016.g1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6088, -1, 6846, -1, 675, -1, 910, -1], 'generators': [1158358440, 1727355720, 3974076856, 2202727080], 'label': '12096.r.504.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '504.m1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.m1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381078
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.d1.a1', '252.h1.b1', '252.i1.b1'], 'contains': ['1008.o1.a1', '1512.n1.a1', '2016.i1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5881, -1, 7341, -1, 840, -1, 551, -1], 'generators': [3974076854, 1158358440, 1727355720, 2202727080], 'label': '12096.r.504.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '504.n1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381079
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.d1.b1', '252.h1.a1', '252.i1.a1'], 'contains': ['1008.o1.a1', '1512.n1.b1', '2016.i1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5881, -1, 6072, -1, 840, -1, 1161, -1], 'generators': [3974076847, 1158358440, 1727355720, 2202727080], 'label': '12096.r.504.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '504.n1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.n1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381080
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '504.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '252.g1.a1', '252.i1.a1', '252.i1.b1'], 'contains': ['1008.o1.a1', '1512.o1.a1', '2016.e1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [4040, -1, 5508, -1, 160, -1, 292, -1], 'generators': [1158358440, 1727355720, 3974076840, 2202727080], 'label': '12096.r.504.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '504.o1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '504.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381081
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '576.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '288.a1.a1', '288.b1.a1', '288.b1.b1', '288.c1.a1', '288.d1.a1', '288.e1.a1', '288.e1.b1'], 'contains': ['1728.a1.a1', '4032.b1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3426, -1, 4819, -1, 1801, -1, 1386, -1], 'generators': [1442090280, 2202727080], 'label': '12096.r.576.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381082
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.a1.a1', '336.a1.a1', '336.a1.b1', '336.d1.a1', '336.f1.a1', '336.f1.b1', '336.h1.a1', '336.i1.a1'], 'contains': ['1344.a1.a1', '2016.a1.a1', '2016.b1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3226, -1, 935, -1, 6867, -1, 7070, -1], 'generators': [3844124776, 763233976, 16], 'label': '12096.r.672.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '672.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381083
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.a1.a1', '336.b1.a1', '336.b1.b1', '336.e1.a1', '336.g1.a1', '336.g1.b1', '336.j1.a1', '336.l1.a1'], 'contains': ['1344.b1.a1', '2016.a1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2880, -1, 1752, -1, 8757, -1, 8941, -1], 'generators': [696851400, 2087786176, 16], 'label': '12096.r.672.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '672.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381084
    {'ambient': '12096.r', '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': '3024.a1.a1', 'complements': ['6048.e1.a1', '6048.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '6.a1.a1', '18.a1.a1', '56.a1.a1', '72.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5527, 3652, 5083, 5351, 2540, 4931, 2553, 3665], 'generators': [1097123063, 2203575127, 7, 16], 'label': '12096.r.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', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 61381085
    {'ambient': '12096.r', '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': '1512.a1.a1', 'complements': ['504.f1.a1', '504.j1.a1', '504.c1.a1', '504.c1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.b1.b1'], 'contains': ['216.f1.a1', '672.h1.a1', '864.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1218, 5548, 4320, 6321, 439, 4590, 501, 4475], 'generators': [2977159680, 3017352960], 'label': '12096.r.24.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['12096.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '12096.r', 'quotient_action_image': '3.1', 'quotient_action_kernel': '8.3', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1512.779'}
  • id: 61381086
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.a1.a1', '336.c1.a1', '336.c1.b1', '336.k1.a1'], 'contains': ['1344.c1.a1', '2016.a1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3654, -1, 181, -1, 9446, -1, 9296, -1], 'generators': [3844124776, 16, 1681587360], 'label': '12096.r.672.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.c1.a1', 'old_label': '672.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381087
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.b1.a1', '336.a1.a1', '336.m1.a1', '336.o1.a1'], 'contains': ['1344.a1.a1', '2016.c1.a1', '2016.d1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [939, -1, 748, -1, 6524, -1, 6956, -1], 'generators': [3844124760, 7, 763233967], 'label': '12096.r.672.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '672.d1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381088
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.b1.b1', '336.a1.b1', '336.m1.b1', '336.o1.b1'], 'contains': ['1344.a1.a1', '2016.c1.b1', '2016.d1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [939, -1, 2550, -1, 6524, -1, 6494, -1], 'generators': [763233965, 5, 3844124765], 'label': '12096.r.672.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '672.d1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.d1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381089
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.b1.a1', '336.b1.a1', '336.n1.a1', '336.p1.a1'], 'contains': ['1344.b1.a1', '2016.c1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [257, -1, 1350, -1, 8617, -1, 8708, -1], 'generators': [696851407, 2087786167, 7], 'label': '12096.r.672.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '672.e1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381090
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.b1.b1', '336.b1.b1', '336.n1.b1', '336.p1.b1'], 'contains': ['1344.b1.a1', '2016.c1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [257, -1, 2334, -1, 8617, -1, 8278, -1], 'generators': [2087786160, 696851405, 5], 'label': '12096.r.672.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '672.e1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381091
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.b1.a1', '336.c1.a1'], 'contains': ['1344.c1.a1', '2016.c1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [1636, -1, 86, -1, 8865, -1, 9015, -1], 'generators': [3844124760, 7, 1681587360], 'label': '12096.r.672.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.a1.a1', 'old_label': '672.f1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381092
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.b1.b1', '336.c1.b1'], 'contains': ['1344.c1.a1', '2016.c1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [1636, -1, 262, -1, 8865, -1, 8515, -1], 'generators': [5, 3844124765, 1681587360], 'label': '12096.r.672.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '112.a1.b1', 'old_label': '672.f1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.f1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381093
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.c1.a1', '336.d1.a1', '336.m1.a1', '336.m1.b1'], 'contains': ['1344.a1.a1', '2016.e1.a1', '2016.f1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [551, -1, 3162, -1, 6027, -1, 6267, -1], 'generators': [3844124760, 1604388960, 763233960], 'label': '12096.r.672.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '672.g1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381094
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '224.c1.a1', '336.e1.a1', '336.n1.a1', '336.n1.b1'], 'contains': ['1344.b1.a1', '2016.f1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [52, -1, 3485, -1, 8168, -1, 8098, -1], 'generators': [696851400, 2087786160, 2933254800], 'label': '12096.r.672.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '672.h1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.h1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381095
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.d1.a1', '336.d1.a1', '336.o1.a1', '336.o1.b1'], 'contains': ['1344.a1.a1', '2016.g1.a1', '2016.h1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [1502, -1, 2652, -1, 6357, -1, 6608, -1], 'generators': [1604388976, 3844124760, 763233960], 'label': '12096.r.672.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '672.i1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381096
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '9.a1.a1'], 'contains': ['54.a1.a1', '54.a1.b1', '54.b1.a1', '189.a1.a1', '216.c1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7836, -1, 6970, -1, 3161, -1, 3738, -1], 'generators': [3604255925, 2453431687, 1574910005, 5, 16, 3129567863, 9], 'label': '12096.r.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '672.1256'}
  • id: 61381097
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.d1.a1', '336.e1.a1', '336.p1.a1', '336.p1.b1'], 'contains': ['1344.b1.a1', '2016.h1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1152, -1, 2760, -1, 8280, -1, 8447, -1], 'generators': [696851400, 2087786160, 2933254816], 'label': '12096.r.672.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '672.j1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.j1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381098
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.e1.a1', '336.f1.a1', '336.m1.b1', '336.o1.b1'], 'contains': ['1344.a1.a1', '2016.i1.a1', '2016.j1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1276, -1, 2049, -1, 6192, -1, 6380, -1], 'generators': [3844124760, 1604388974, 763233960], 'label': '12096.r.672.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.b1', 'old_label': '672.k1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381099
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.e1.b1', '336.f1.b1', '336.m1.a1', '336.o1.a1'], 'contains': ['1344.a1.a1', '2016.i1.b1', '2016.j1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1276, -1, 645, -1, 6192, -1, 6843, -1], 'generators': [1604388967, 3844124760, 763233960], 'label': '12096.r.672.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '672.k1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.k1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381100
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.e1.a1', '336.g1.a1', '336.n1.b1', '336.p1.b1'], 'contains': ['1344.b1.a1', '2016.j1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [427, -1, 2989, -1, 8480, -1, 8193, -1], 'generators': [696851400, 2087786160, 2933254814], 'label': '12096.r.672.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '672.l1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.l1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381101
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '672.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.e1.b1', '336.g1.b1', '336.n1.a1', '336.p1.a1'], 'contains': ['1344.b1.a1', '2016.j1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [427, -1, 2228, -1, 8480, -1, 8601, -1], 'generators': [696851400, 2087786160, 2933254823], 'label': '12096.r.672.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '672.l1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.l1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381102
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['378.a1.a1', '378.c1.a1'], 'contains': ['1512.b1.a1', '1512.c1.a1', '1512.d1.a1', '1512.f1.a1', '1512.i1.a1', '1512.i1.a2'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [7557, -1, 9946, -1, 4679, -1, 5082, -1], 'generators': [3604255925, 1574910005, 7, 16], 'label': '12096.r.756.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '756.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381103
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['378.a1.b1', '378.c1.a1'], 'contains': ['1512.b1.b1', '1512.c1.b1', '1512.d1.b1', '1512.f1.a1', '1512.i1.a1', '1512.i1.a2'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 189, 'diagramx': [7557, -1, 9704, -1, 4679, -1, 4968, -1], 'generators': [1574910005, 5, 16, 3604255927], 'label': '12096.r.756.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '756.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381104
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.a1.a1', '378.a1.a1', '378.b1.a1', '378.c1.a1'], 'contains': ['1512.b1.a1', '1512.d1.b1', '1512.g1.a1', '1512.j1.a1', '1512.k1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6824, -1, 9347, -1, 2062, -1, 3218, -1], 'generators': [1574910000, 3604255920, 7, 16], 'label': '12096.r.756.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '756.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381105
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.a1.b1', '378.a1.b1', '378.b1.b1', '378.c1.a1'], 'contains': ['1512.b1.b1', '1512.d1.a1', '1512.g1.a1', '1512.j1.b1', '1512.k1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 63, 'diagramx': [6824, -1, 9009, -1, 2062, -1, 2437, -1], 'generators': [3604255925, 1574910005, 5, 16], 'label': '12096.r.756.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '756.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381106
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '252.b1.a1', '252.c1.a1', '378.c1.a1'], 'contains': ['1512.a1.a1', '1512.b1.a1', '1512.b1.b1', '1512.c1.a1', '1512.c1.b1', '1512.e1.a1', '1512.h1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [9006, -1, 7629, -1, 5622, -1, 5541, -1], 'generators': [3604255925, 5, 16, 9], 'label': '12096.r.756.c1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '756.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381107
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['56.a1.a1', '56.a1.b1', '56.b1.a1', '56.b1.b1', '56.c1.a1', '56.d1.a1', '56.e1.a1', '84.a1.a1', '84.b1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3983, -1, 2553, -1, 8502, -1, 8686, -1], 'generators': [1604388978, 3844124774, 5, 16, 1681587360, 763233983, 9], 'label': '12096.r.28.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '28.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.111'}
  • id: 61381108
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['378.c1.a1', '378.d1.a1'], 'contains': ['1512.d1.a1', '1512.d1.b1', '1512.e1.a1', '1512.h1.a1', '1512.i1.a1', '1512.i1.a2'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [8389, -1, 9452, -1, 5254, -1, 5197, -1], 'generators': [3604255925, 1574910005, 16, 9], 'label': '12096.r.756.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '756.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381109
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['378.a1.a1', '378.a1.b1', '378.d1.a1'], 'contains': ['1512.d1.a1', '1512.d1.b1', '1512.f1.a1', '1512.i1.a1', '1512.i1.a2'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [7720, -1, 9813, -1, 4511, -1, 4607, -1], 'generators': [1574910005, 3604255929, 16, 3129567863], 'label': '12096.r.756.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '756.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381110
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['378.a1.a1', '378.a1.b1', '378.d1.a1'], 'contains': ['1512.d1.a1', '1512.d1.b1', '1512.f1.a1', '1512.i1.a1', '1512.i1.a2'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [7720, -1, 9591, -1, 4511, -1, 4722, -1], 'generators': [3604255925, 1574910005, 16, 3129567863], 'label': '12096.r.756.e1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '756.e1.a2', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.e1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381111
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.d1.a1', '378.a1.a1', '378.b1.b1', '378.d1.a1'], 'contains': ['1512.d1.a1', '1512.g1.a1', '1512.l1.a1', '1512.n1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6967, -1, 8815, -1, 1185, -1, 2255, -1], 'generators': [3604255925, 1574910005, 16, 3129567845], 'label': '12096.r.756.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '756.f1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381112
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.d1.b1', '378.a1.b1', '378.b1.a1', '378.d1.a1'], 'contains': ['1512.d1.b1', '1512.g1.a1', '1512.l1.b1', '1512.n1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6967, -1, 8679, -1, 1185, -1, 2506, -1], 'generators': [1574910000, 3604255920, 16, 3129567863], 'label': '12096.r.756.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '756.f1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.f1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381113
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.e1.a1', '378.c1.a1', '378.d1.a1', '378.e1.a1'], 'contains': ['1512.e1.a1', '1512.f1.a1', '1512.g1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7941, -1, 9228, -1, 4907, -1, 4845, -1], 'generators': [1574910000, 3604255920, 16, 9], 'label': '12096.r.756.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '756.g1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381114
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.f1.a1', '378.a1.a1', '378.a1.b1', '378.e1.a1'], 'contains': ['1512.f1.a1', '1512.g1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7382, -1, 9106, -1, 2938, -1, 4320, -1], 'generators': [1574910000, 3604255920, 16, 3129567849], 'label': '12096.r.756.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '756.h1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381115
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '189.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '252.g1.a1', '378.b1.a1', '378.b1.b1', '378.e1.a1'], 'contains': ['1512.g1.a1', '1512.m1.a1', '1512.o1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6586, -1, 7138, -1, 394, -1, 1070, -1], 'generators': [1574910000, 3604255920, 16, 3129567856], 'label': '12096.r.756.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '756.i1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.i1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 61381116
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.h1.a1', '378.b1.a1'], 'contains': ['1512.j1.a1', '1512.k1.a1', '1512.l1.b1', '1512.m1.a1', '1512.n1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [6343, -1, 6058, -1, 495, -1, 1655, -1], 'generators': [1574910000, 3604255920, 7, 3129567863], 'label': '12096.r.756.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '756.j1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.j1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381117
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['252.h1.b1', '378.b1.b1'], 'contains': ['1512.j1.b1', '1512.k1.b1', '1512.l1.a1', '1512.m1.a1', '1512.n1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [6343, -1, 7542, -1, 495, -1, 755, -1], 'generators': [1574910005, 5, 3604255934, 3129567845], 'label': '12096.r.756.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '756.j1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.j1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381118
    {'ambient': '12096.r', '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': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['72.a1.a1', '72.a1.b1', '72.b1.a1', '72.b1.b1', '72.c1.a1', '72.d1.a1', '72.e1.a1', '108.a1.a1', '252.b1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8918, -1, 6866, -1, 4011, -1, 3593, -1], 'generators': [125319729, 1038009005, 204791765, 5, 16, 9], 'label': '12096.r.36.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '10000.dk', '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': '168.47'}
  • id: 61381119
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '252.i1.a1', '378.b1.a1'], 'contains': ['1512.k1.a1', '1512.n1.b1', '1512.o1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3974, -1, 4965, -1, 294, -1, 1001, -1], 'generators': [1574910000, 3604255920, 3129567847, 7], 'label': '12096.r.756.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '756.k1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.k1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 61381120
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '756.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.b1', '252.i1.b1', '378.b1.b1'], 'contains': ['1512.k1.b1', '1512.n1.a1', '1512.o1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3974, -1, 6149, -1, 294, -1, 201, -1], 'generators': [3604255925, 1574910005, 5, 3129567845], 'label': '12096.r.756.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '756.k1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '756.k1.b1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 61381121
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '864.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '288.a1.a1', '432.a1.a1', '432.a1.b1', '432.b1.a1', '432.c1.a1', '432.c1.b1', '432.d1.a1', '432.e1.a1'], 'contains': ['1728.a1.a1', '6048.a1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9353, -1, 6533, -1, 3083, -1, 3057, -1], 'generators': [16, 2453431680], 'label': '12096.r.864.a1.a1', 'mobius_quo': None, 'mobius_sub': -4, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '864.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381123
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.b1', '288.b1.b1', '432.a1.b1', '432.f1.b1', '432.g1.b1'], 'contains': ['1728.a1.a1', '6048.b1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2540, -1, 5296, -1, 1911, -1, 964, -1], 'generators': [2453431685, 5], 'label': '12096.r.864.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.b1', 'old_label': '864.b1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381124
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '864.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '288.c1.a1', '432.b1.a1', '432.f1.a1', '432.f1.b1'], 'contains': ['1728.a1.a1', '6048.c1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1973, -1, 4330, -1, 1358, -1, 1257, -1], 'generators': [1099567560, 999821640], 'label': '12096.r.864.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '864.c1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.c1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381125
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.d1.a1', '432.b1.a1', '432.g1.a1', '432.g1.b1'], 'contains': ['1728.a1.a1', '6048.d1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5192, -1, 5111, -1, 2097, -1, 1908, -1], 'generators': [1099567560, 999821656], 'label': '12096.r.864.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '864.d1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381126
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.e1.a1', '432.c1.a1', '432.f1.b1', '432.g1.b1'], 'contains': ['1728.a1.a1', '6048.e1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4699, -1, 5360, -1, 2009, -1, 1317, -1], 'generators': [1099567560, 999821654], 'label': '12096.r.864.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.b1', 'old_label': '864.e1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381127
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '864.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.e1.b1', '432.c1.b1', '432.f1.a1', '432.g1.a1'], 'contains': ['1728.a1.a1', '6048.e1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4699, -1, 4539, -1, 2009, -1, 2092, -1], 'generators': [1099567560, 999821647], 'label': '12096.r.864.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '864.e1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.e1.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381128
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.a1.a1', '336.b1.a1', '336.c1.a1', '504.b1.a1', '504.d1.a1', '504.e1.a1'], 'contains': ['2016.a1.a1', '2016.c1.a1', '3024.a1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3529, -1, 1224, -1, 7210, -1, 7676, -1], 'generators': [2087786183, 7, 16], 'label': '12096.r.1008.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '1008.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381129
    {'ambient': '12096.r', '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': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '18.a1.a1', '18.a1.b1', '18.b1.a1'], 'contains': ['72.f1.a1', '108.b1.a1', '252.g1.a1', '288.a1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6619, -1, 5757, -1, 1230, -1, 1498, -1], 'generators': [1158358440, 1727355720, 1442090280, 3974076840, 16, 2202727096], 'label': '12096.r.36.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '10000.dk', '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': '168.43'}
  • id: 61381130
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.a1.b1', '336.b1.b1', '336.c1.b1', '504.b1.b1', '504.d1.b1', '504.e1.a1'], 'contains': ['2016.a1.a1', '2016.c1.b1', '3024.a1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [3529, -1, 1066, -1, 7210, -1, 7425, -1], 'generators': [2087786176, 5, 16], 'label': '12096.r.1008.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '1008.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381131
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '252.a1.a1', '336.a1.a1', '504.a1.a1', '504.c1.a1', '504.f1.a1'], 'contains': ['2016.b1.a1', '2016.d1.a1', '3024.a1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [7758, -1, 6766, -1, 3909, -1, 4658, -1], 'generators': [2202727103, 7, 16], 'label': '12096.r.1008.b1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '1008.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381132
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.b1', '252.a1.b1', '336.a1.b1', '504.a1.b1', '504.c1.b1', '504.f1.a1'], 'contains': ['2016.b1.a1', '2016.d1.b1', '3024.a1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [7758, -1, 8098, -1, 3909, -1, 4087, -1], 'generators': [5, 16, 2202727085], 'label': '12096.r.1008.b1.b1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '1008.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381133
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '252.g1.a1', '336.d1.a1', '504.a1.a1', '504.a1.b1', '504.g1.a1'], 'contains': ['2016.b1.a1', '2016.e1.a1', '2016.g1.a1', '3024.c1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [6195, -1, 6125, -1, 3476, -1, 3722, -1], 'generators': [3974076840, 16, 2202727096], 'label': '12096.r.1008.c1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '1008.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381134
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.d1.a1', '336.e1.a1', '504.b1.a1', '504.b1.b1', '504.h1.a1'], 'contains': ['2016.a1.a1', '2016.f1.a1', '2016.h1.a1', '3024.c1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2329, -1, 3832, -1, 6994, -1, 7217, -1], 'generators': [2087786176, 16, 2933254816], 'label': '12096.r.1008.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '1008.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381135
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '252.d1.a1', '336.f1.a1', '504.a1.b1', '504.c1.a1', '504.j1.a1'], 'contains': ['2016.b1.a1', '2016.i1.a1', '3024.d1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [7965, -1, 7750, -1, 3742, -1, 3973, -1], 'generators': [3974076854, 16, 2202727096], 'label': '12096.r.1008.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '1008.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381136
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.b1', '252.d1.b1', '336.f1.b1', '504.a1.a1', '504.c1.b1', '504.j1.a1'], 'contains': ['2016.b1.a1', '2016.i1.b1', '3024.d1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [7965, -1, 7910, -1, 3742, -1, 4544, -1], 'generators': [3974076847, 16, 2202727096], 'label': '12096.r.1008.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '1008.e1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.e1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381137
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.f1.a1', '336.g1.a1', '504.b1.b1', '504.d1.a1', '504.k1.a1'], 'contains': ['2016.a1.a1', '2016.j1.a1', '3024.d1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3147, -1, 2856, -1, 7082, -1, 7278, -1], 'generators': [2087786176, 16, 2933254814], 'label': '12096.r.1008.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '1008.f1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381138
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.f1.b1', '336.g1.b1', '504.b1.a1', '504.d1.b1', '504.k1.a1'], 'contains': ['2016.a1.a1', '2016.j1.b1', '3024.d1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [3147, -1, 2501, -1, 7082, -1, 7512, -1], 'generators': [2087786176, 2933254823, 16], 'label': '12096.r.1008.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '1008.f1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.f1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381139
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.h1.a1', '336.j1.a1', '336.k1.a1', '504.e1.a1', '504.h1.a1', '504.k1.a1'], 'contains': ['2016.a1.a1', '3024.b1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4362, -1, 1385, -1, 7759, -1, 7799, -1], 'generators': [2087786169, 16, 9], 'label': '12096.r.1008.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '1008.g1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381140
    {'ambient': '12096.r', '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': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '18.a1.a1'], 'contains': ['72.f1.a1', '108.c1.a1', '252.i1.a1', '288.b1.a1'], 'core': '12096.a1.a1', 'coset_action_label': '36T9588', 'count': 18, 'diagramx': [1630, -1, 4593, -1, 894, -1, 1011, -1], 'generators': [3974076847, 2202727087, 1727355720, 1442090280, 7, 1158358447], 'label': '12096.r.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '12096.r', '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': '168.43'}
  • id: 61381177
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['756.f1.b1', '756.j1.a1'], 'contains': ['3024.h1.a1', '3024.i1.b1', '3024.k1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [6447, -1, 7374, -1, 1118, -1, 2434, -1], 'generators': [3604255936, 1574910000, 3129567863], 'label': '12096.r.1512.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '378.b1.a1', 'old_label': '1512.l1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.l1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381141
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.i1.a1', '336.l1.a1', '504.d1.a1', '504.d1.b1', '504.h1.a1'], 'contains': ['2016.a1.a1', '3024.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4470, -1, 1860, -1, 7350, -1, 7581, -1], 'generators': [2087786176, 2933254818, 16], 'label': '12096.r.1008.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '1008.h1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381142
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '252.e1.a1', '336.h1.a1', '504.f1.a1', '504.g1.a1', '504.j1.a1'], 'contains': ['2016.b1.a1', '3024.b1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [8735, -1, 8409, -1, 5496, -1, 5426, -1], 'generators': [2202727089, 16, 9], 'label': '12096.r.1008.i1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '1008.i1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381143
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '252.f1.a1', '336.i1.a1', '504.c1.a1', '504.c1.b1', '504.g1.a1'], 'contains': ['2016.b1.a1', '3024.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [8343, -1, 8280, -1, 4757, -1, 5333, -1], 'generators': [16, 3974076858, 2202727096], 'label': '12096.r.1008.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '1008.j1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381144
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1.a1', '252.i1.a1', '336.m1.a1', '504.a1.a1'], 'contains': ['2016.d1.a1', '2016.e1.a1', '2016.i1.b1', '3024.f1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [2702, -1, 4903, -1, 2373, -1, 3363, -1], 'generators': [3974076847, 2202727087, 7], 'label': '12096.r.1008.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '504.a1.a1', 'old_label': '1008.k1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381145
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1.b1', '252.i1.b1', '336.m1.b1', '504.a1.b1'], 'contains': ['2016.d1.b1', '2016.e1.a1', '2016.i1.a1', '3024.f1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [2702, -1, 5336, -1, 2373, -1, 1606, -1], 'generators': [3974076854, 14, 2202727094], 'label': '12096.r.1008.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '504.a1.b1', 'old_label': '1008.k1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381146
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.m1.a1', '336.n1.a1', '504.b1.a1'], 'contains': ['2016.c1.a1', '2016.f1.a1', '2016.j1.b1', '3024.f1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1212, -1, 3142, -1, 6651, -1, 7157, -1], 'generators': [23, 2087786183, 2933254800], 'label': '12096.r.1008.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '1008.l1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381147
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.m1.b1', '336.n1.b1', '504.b1.b1'], 'contains': ['2016.c1.b1', '2016.f1.a1', '2016.j1.a1', '3024.f1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1212, -1, 3529, -1, 6651, -1, 6695, -1], 'generators': [2087786160, 5, 2933254805], 'label': '12096.r.1008.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.b1', 'old_label': '1008.l1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.l1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381148
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1.a1', '252.h1.a1', '336.o1.a1', '504.a1.a1'], 'contains': ['2016.d1.a1', '2016.g1.a1', '2016.i1.b1', '3024.g1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [4988, -1, 5111, -1, 2539, -1, 3508, -1], 'generators': [3974076847, 23, 2202727103], 'label': '12096.r.1008.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '504.a1.a1', 'old_label': '1008.m1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381149
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1.b1', '252.h1.b1', '336.o1.b1', '504.a1.b1'], 'contains': ['2016.d1.b1', '2016.g1.a1', '2016.i1.a1', '3024.g1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [4988, -1, 6635, -1, 2539, -1, 2242, -1], 'generators': [3974076854, 5, 2202727085], 'label': '12096.r.1008.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '504.a1.b1', 'old_label': '1008.m1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.m1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381150
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.o1.a1', '336.p1.a1', '504.b1.a1'], 'contains': ['2016.c1.a1', '2016.h1.a1', '2016.j1.b1', '3024.g1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1455, -1, 1474, -1, 6739, -1, 7338, -1], 'generators': [23, 2087786183, 2933254816], 'label': '12096.r.1008.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '1008.n1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381151
    {'ambient': '12096.r', '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': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '18.a1.b1'], 'contains': ['72.f1.a1', '108.c1.b1', '252.i1.b1', '288.b1.b1'], 'core': '12096.a1.a1', 'coset_action_label': '36T9588', 'count': 18, 'diagramx': [1630, -1, 5507, -1, 894, -1, 405, -1], 'generators': [3974076845, 1442090280, 1727355725, 5, 1158358445, 2202727085], 'label': '12096.r.36.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.c1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 61381152
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['336.o1.b1', '336.p1.b1', '504.b1.b1'], 'contains': ['2016.c1.b1', '2016.h1.a1', '2016.j1.a1', '3024.g1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1455, -1, 3227, -1, 6739, -1, 6755, -1], 'generators': [2087786160, 5, 2933254814], 'label': '12096.r.1008.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.b1', 'old_label': '1008.n1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381153
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1008.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.i1.a1', '504.l1.a1', '504.l1.b1', '504.m1.a1', '504.n1.a1', '504.n1.b1', '504.o1.a1'], 'contains': ['3024.j1.a1', '4032.b1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [5844, -1, 6499, -1, 923, -1, 1261, -1], 'generators': [1158358440, 1727355720, 2202727080], 'label': '12096.r.1008.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '1008.o1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1008.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 61381154
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1344.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['448.a1.a1', '672.a1.a1', '672.d1.a1', '672.d1.b1', '672.g1.a1', '672.i1.a1', '672.k1.a1', '672.k1.b1'], 'contains': ['4032.a1.a1', '4032.b1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1002, -1, 2085, -1, 6458, -1, 6619, -1], 'generators': [3844124760, 763233960], 'label': '12096.r.1344.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '1344.a1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381155
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1344.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['448.a1.a1', '672.b1.a1', '672.e1.a1', '672.e1.b1', '672.h1.a1', '672.j1.a1', '672.l1.a1', '672.l1.b1'], 'contains': ['4032.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [437, -1, 2285, -1, 8380, -1, 8379, -1], 'generators': [696851400, 2087786160], 'label': '12096.r.1344.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '1344.b1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381156
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1344.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['448.a1.a1', '672.c1.a1', '672.f1.a1', '672.f1.b1'], 'contains': ['4032.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1750, -1, 238, -1, 8663, -1, 8515, -1], 'generators': [3844124760, 1681587360], 'label': '12096.r.1344.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.c1.a1', 'old_label': '1344.c1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1344.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381157
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': ['8.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '504.e1.a1', '504.f1.a1', '756.c1.a1'], 'contains': ['3024.a1.a1', '3024.a1.b1', '3024.b1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8751, 1005, 8125, 3403, 5600, 9645, 5493, 9736], 'generators': [5, 16, 9], 'label': '12096.r.1512.a1.a1', 'mobius_quo': 0, 'mobius_sub': 504, 'normal_closure': '1512.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['3024.a1.a1', '3024.a1.b1', '3024.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1512.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1512.779', 'quotient_action_kernel_order': 1512, 'quotient_fusion': None, 'short_label': '1512.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381158
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '504.a1.a1', '504.b1.a1', '756.a1.a1', '756.b1.a1', '756.c1.a1'], 'contains': ['3024.a1.a1', '3024.c1.a1', '3024.d1.b1', '3024.f1.a1', '3024.g1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6614, -1, 6357, -1, 3609, -1, 4339, -1], 'generators': [3604255920, 7, 16], 'label': '12096.r.1512.b1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '1512.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381159
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.b1', '504.a1.b1', '504.b1.b1', '756.a1.b1', '756.b1.b1', '756.c1.a1'], 'contains': ['3024.a1.b1', '3024.c1.a1', '3024.d1.a1', '3024.f1.b1', '3024.g1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 63, 'diagramx': [6614, -1, 7231, -1, 3609, -1, 3814, -1], 'generators': [3604255925, 5, 16], 'label': '12096.r.1512.b1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '1512.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381160
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '504.c1.a1', '504.d1.a1', '756.a1.a1', '756.c1.a1'], 'contains': ['3024.a1.a1', '3024.d1.a1', '3024.e1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [8372, -1, 7644, -1, 4855, -1, 5088, -1], 'generators': [3604255925, 7, 16], 'label': '12096.r.1512.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '1512.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381161
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.b1', '504.c1.b1', '504.d1.b1', '756.a1.b1', '756.c1.a1'], 'contains': ['3024.a1.b1', '3024.d1.b1', '3024.e1.a1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 63, 'diagramx': [8372, -1, 7507, -1, 4855, -1, 4961, -1], 'generators': [5, 16, 3604255927], 'label': '12096.r.1512.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '1512.c1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381162
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '18.a1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.c1.a1', '378.b1.a1', '432.a1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6777, -1, 5291, -1, 1694, -1, 1847, -1], 'generators': [2453431687, 1574910000, 3604255920, 7, 16, 3129567863], 'label': '12096.r.54.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 61381163
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['756.a1.a1', '756.b1.b1', '756.d1.a1', '756.e1.a1', '756.e1.a2', '756.f1.a1'], 'contains': ['3024.c1.a1', '3024.d1.a1', '3024.i1.a1', '3024.k1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [7293, -1, 9195, -1, 3342, -1, 3631, -1], 'generators': [3604255925, 1574910005, 16], 'label': '12096.r.1512.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '1512.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381164
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['756.a1.b1', '756.b1.a1', '756.d1.a1', '756.e1.a1', '756.e1.a2', '756.f1.b1'], 'contains': ['3024.c1.a1', '3024.d1.b1', '3024.i1.b1', '3024.k1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [7293, -1, 9398, -1, 3342, -1, 3882, -1], 'generators': [1574910000, 16, 3604255927], 'label': '12096.r.1512.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '1512.d1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381165
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '504.g1.a1', '504.h1.a1', '756.c1.a1', '756.d1.a1', '756.g1.a1'], 'contains': ['3024.b1.a1', '3024.c1.a1', '3024.e1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [8620, -1, 8566, -1, 5254, -1, 5189, -1], 'generators': [3604255920, 16, 9], 'label': '12096.r.1512.e1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '1512.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381166
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['756.a1.a1', '756.a1.b1', '756.e1.a1', '756.e1.a2', '756.g1.a1', '756.h1.a1'], 'contains': ['3024.c1.a1', '3024.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [7541, -1, 9584, -1, 4521, -1, 4430, -1], 'generators': [1574910000, 3604255929, 16], 'label': '12096.r.1512.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '1512.f1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381167
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '189.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.i1.a1', '756.b1.a1', '756.b1.b1', '756.f1.a1', '756.f1.b1', '756.g1.a1', '756.h1.a1', '756.i1.a1'], 'contains': ['3024.c1.a1', '3024.h1.a1', '3024.j1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6931, -1, 9037, -1, 1656, -1, 2917, -1], 'generators': [1574910000, 3604255920, 16], 'label': '12096.r.1512.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '1512.g1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.g1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381168
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '504.j1.a1', '504.k1.a1', '756.c1.a1', '756.d1.a1'], 'contains': ['3024.b1.a1', '3024.d1.a1', '3024.d1.b1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [9118, -1, 7561, -1, 5387, -1, 5028, -1], 'generators': [3604255925, 16, 9], 'label': '12096.r.1512.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '1512.h1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381169
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['756.a1.a1', '756.a1.b1', '756.d1.a1', '756.e1.a1', '756.e1.a2'], 'contains': ['3024.d1.a1', '3024.d1.b1', '3024.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [8146, -1, 9727, -1, 4659, -1, 4887, -1], 'generators': [1574910005, 16, 3604255927], 'label': '12096.r.1512.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '1512.i1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381170
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['756.a1.a1', '756.a1.b1', '756.d1.a1', '756.e1.a1', '756.e1.a2'], 'contains': ['3024.d1.a1', '3024.d1.b1', '3024.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [8146, -1, 9904, -1, 4659, -1, 4800, -1], 'generators': [1574910005, 3604255929, 16], 'label': '12096.r.1512.i1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '1512.i1.a2', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.i1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 61381171
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['756.b1.a1', '756.j1.a1'], 'contains': ['3024.f1.a1', '3024.g1.a1', '3024.h1.a1', '3024.i1.b1', '3024.k1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [6087, -1, 7064, -1, 1463, -1, 2985, -1], 'generators': [3604255936, 1574910000, 7], 'label': '12096.r.1512.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '378.b1.a1', 'old_label': '1512.j1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381172
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['756.b1.b1', '756.j1.b1'], 'contains': ['3024.f1.b1', '3024.g1.b1', '3024.h1.a1', '3024.i1.a1', '3024.k1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [6087, -1, 8226, -1, 1463, -1, 1798, -1], 'generators': [1574910005, 5, 3604255934], 'label': '12096.r.1512.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '378.b1.b1', 'old_label': '1512.j1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381173
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '18.a1.b1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.c1.b1', '378.b1.b1', '432.a1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6777, -1, 6098, -1, 1694, -1, 1363, -1], 'generators': [2453431694, 3604255925, 1574910005, 5, 16, 3129567845], 'label': '12096.r.54.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.b1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 61381174
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.l1.a1', '756.b1.a1', '756.j1.a1', '756.k1.a1'], 'contains': ['3024.f1.a1', '3024.i1.b1', '3024.j1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5598, -1, 6068, -1, 1017, -1, 2365, -1], 'generators': [1574910000, 3604255920, 7], 'label': '12096.r.1512.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '1512.k1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.k1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381175
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.l1.b1', '756.b1.b1', '756.j1.b1', '756.k1.b1'], 'contains': ['3024.f1.b1', '3024.i1.a1', '3024.j1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5598, -1, 7003, -1, 1017, -1, 1165, -1], 'generators': [3604255925, 1574910005, 5], 'label': '12096.r.1512.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '1512.k1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.k1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381176
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['756.f1.a1', '756.j1.b1'], 'contains': ['3024.h1.a1', '3024.i1.a1', '3024.k1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [6447, -1, 8341, -1, 1118, -1, 1729, -1], 'generators': [1574910005, 3604255934, 3129567845], 'label': '12096.r.1512.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '378.b1.b1', 'old_label': '1512.l1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381178
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '189.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.m1.a1', '756.i1.a1', '756.j1.a1', '756.j1.b1'], 'contains': ['3024.h1.a1', '3024.j1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [5989, -1, 6827, -1, 675, -1, 1326, -1], 'generators': [1574910000, 3604255920, 3129567856], 'label': '12096.r.1512.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '1512.m1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.m1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381179
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.n1.a1', '756.f1.a1', '756.j1.b1', '756.k1.b1'], 'contains': ['3024.i1.a1', '3024.j1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5854, -1, 7170, -1, 829, -1, 1096, -1], 'generators': [3604255925, 1574910005, 3129567845], 'label': '12096.r.1512.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '1512.n1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.n1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381180
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['504.n1.b1', '756.f1.b1', '756.j1.a1', '756.k1.a1'], 'contains': ['3024.i1.b1', '3024.j1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [5854, -1, 5978, -1, 829, -1, 1455, -1], 'generators': [1574910000, 3604255920, 3129567863], 'label': '12096.r.1512.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '1512.n1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.n1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381181
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1512.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '189.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '504.o1.a1', '756.i1.a1', '756.k1.a1', '756.k1.b1'], 'contains': ['3024.j1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3922, -1, 5673, -1, 294, -1, 832, -1], 'generators': [3129567840, 1574910000, 3604255920], 'label': '12096.r.1512.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '1512.o1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1512.o1.a1', 'subgroup_fusion': None, 'weyl_group': '21.1'}
  • id: 61381182
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '1728.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '576.a1.a1', '864.a1.a1', '864.b1.a1', '864.b1.b1', '864.c1.a1', '864.d1.a1', '864.e1.a1', '864.e1.b1'], 'contains': ['12096.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3638, -1, 4658, -1, 1960, -1, 1668, -1], 'generators': [2453431680], 'label': '12096.r.1728.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '1728.a1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 61381183
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.a1.a1', '672.b1.a1', '672.c1.a1', '1008.a1.a1', '1008.a1.b1', '1008.d1.a1', '1008.f1.a1', '1008.f1.b1', '1008.g1.a1', '1008.h1.a1'], 'contains': ['4032.a1.a1', '6048.a1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2942, -1, 1484, -1, 7146, -1, 7468, -1], 'generators': [2087786176, 16], 'label': '12096.r.2016.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '2016.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381184
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '18.b1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '378.e1.a1', '432.d1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7563, -1, 7846, -1, 2843, -1, 4053, -1], 'generators': [2453431698, 1574910000, 3604255920, 16, 3129567849, 9], 'label': '12096.r.54.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '336.210'}
  • id: 61381185
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '504.i1.a1', '672.a1.a1', '1008.b1.a1', '1008.b1.b1', '1008.c1.a1', '1008.e1.a1', '1008.e1.b1', '1008.i1.a1', '1008.j1.a1'], 'contains': ['4032.b1.a1', '6048.a1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [7836, -1, 7821, -1, 3714, -1, 4153, -1], 'generators': [16, 2202727096], 'label': '12096.r.2016.b1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '2016.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381186
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.d1.a1', '672.e1.a1', '672.f1.a1', '1008.a1.a1', '1008.l1.a1', '1008.n1.a1'], 'contains': ['4032.a1.a1', '6048.b1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1189, -1, 1232, -1, 6872, -1, 7278, -1], 'generators': [2087786167, 7], 'label': '12096.r.2016.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '2016.c1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381187
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '112.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.d1.b1', '672.e1.b1', '672.f1.b1', '1008.a1.b1', '1008.l1.b1', '1008.n1.b1'], 'contains': ['4032.a1.a1', '6048.b1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1189, -1, 2426, -1, 6872, -1, 7041, -1], 'generators': [2087786160, 5], 'label': '12096.r.2016.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '2016.c1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381188
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.b1.a1', '504.l1.a1', '672.d1.a1', '1008.b1.a1', '1008.k1.a1', '1008.m1.a1'], 'contains': ['4032.b1.a1', '6048.b1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [4274, -1, 4975, -1, 2650, -1, 3363, -1], 'generators': [2202727087, 7], 'label': '12096.r.2016.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '2016.d1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381189
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '168.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.b1.b1', '504.l1.b1', '672.d1.b1', '1008.b1.b1', '1008.k1.b1', '1008.m1.b1'], 'contains': ['4032.b1.a1', '6048.b1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [4274, -1, 5560, -1, 2650, -1, 2213, -1], 'generators': [5, 2202727085], 'label': '12096.r.2016.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.b1', 'old_label': '2016.d1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381190
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.c1.a1', '504.o1.a1', '672.g1.a1', '1008.c1.a1', '1008.k1.a1', '1008.k1.b1'], 'contains': ['4032.b1.a1', '6048.c1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [2288, -1, 4921, -1, 2185, -1, 2152, -1], 'generators': [3974076840, 2202727080], 'label': '12096.r.2016.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '2016.e1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381191
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.g1.a1', '672.h1.a1', '1008.d1.a1', '1008.l1.a1', '1008.l1.b1'], 'contains': ['4032.a1.a1', '6048.c1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [574, -1, 3472, -1, 6607, -1, 6750, -1], 'generators': [2087786160, 2933254800], 'label': '12096.r.2016.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '2016.f1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381192
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '252.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.d1.a1', '504.m1.a1', '672.i1.a1', '1008.c1.a1', '1008.m1.a1', '1008.m1.b1'], 'contains': ['4032.b1.a1', '6048.d1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 252, 'diagramx': [5311, -1, 5467, -1, 2562, -1, 2613, -1], 'generators': [3974076856, 2202727080], 'label': '12096.r.2016.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '252.b1.a1', 'old_label': '2016.g1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381193
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.i1.a1', '672.j1.a1', '1008.d1.a1', '1008.n1.a1', '1008.n1.b1'], 'contains': ['4032.a1.a1', '6048.d1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [1606, -1, 2643, -1, 6783, -1, 6981, -1], 'generators': [2087786160, 2933254816], 'label': '12096.r.2016.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '2016.h1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381194
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.e1.a1', '504.n1.a1', '672.k1.a1', '1008.e1.a1', '1008.k1.b1', '1008.m1.b1'], 'contains': ['4032.b1.a1', '6048.e1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [4649, -1, 6088, -1, 2474, -1, 2410, -1], 'generators': [3974076854, 2202727080], 'label': '12096.r.2016.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '504.a1.b1', 'old_label': '2016.i1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381195
    {'ambient': '12096.r', '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': '3024.a1.b1', 'complements': ['6048.e1.b1', '6048.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.b1', '6.a1.b1', '18.a1.b1', '56.a1.b1', '72.a1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5527, 3652, 5624, 2476, 2540, 4931, 2122, 6301], 'generators': [2203575134, 1097123056, 5, 16], 'label': '12096.r.2.a1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 61381196
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '28.a1.a1'], 'contains': ['112.a1.a1', '112.b1.a1', '112.c1.b1', '112.f1.a1', '112.g1.a1', '168.a1.a1', '168.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2483, -1, 2357, -1, 8202, -1, 8479, -1], 'generators': [3844124776, 1604388967, 7, 16, 1681587360, 763233983], 'label': '12096.r.56.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381197
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '504.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.e1.b1', '504.n1.b1', '672.k1.b1', '1008.e1.b1', '1008.k1.a1', '1008.m1.a1'], 'contains': ['4032.b1.a1', '6048.e1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 504, 'diagramx': [4649, -1, 5117, -1, 2474, -1, 3275, -1], 'generators': [3974076847, 2202727080], 'label': '12096.r.2016.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '504.a1.a1', 'old_label': '2016.i1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381198
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.k1.a1', '672.l1.a1', '1008.f1.a1', '1008.l1.b1', '1008.n1.b1'], 'contains': ['4032.a1.a1', '6048.e1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1303, -1, 2971, -1, 6695, -1, 6811, -1], 'generators': [2087786160, 2933254814], 'label': '12096.r.2016.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.b1', 'old_label': '2016.j1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381199
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '2016.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['672.k1.b1', '672.l1.b1', '1008.f1.b1', '1008.l1.a1', '1008.n1.a1'], 'contains': ['4032.a1.a1', '6048.e1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1303, -1, 2202, -1, 6695, -1, 7157, -1], 'generators': [2087786160, 2933254823], 'label': '12096.r.2016.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '168.a1.a1', 'old_label': '2016.j1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2016.j1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 61381200
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.a1', 'complements': ['4.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '1008.a1.a1', '1008.b1.a1', '1512.a1.a1', '1512.b1.a1', '1512.c1.a1'], 'contains': ['6048.a1.a1', '6048.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8036, 1903, 6346, 4137, 3909, 7597, 4636, 6642], 'generators': [7, 16], 'label': '12096.r.3024.a1.a1', 'mobius_quo': 0, 'mobius_sub': -504, 'normal_closure': '3024.a1.a1', 'normal_contained_in': ['6.a1.a1', '1512.a1.a1'], 'normal_contains': ['6048.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3024.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1512.779', 'quotient_action_kernel_order': 1512, 'quotient_fusion': None, 'short_label': '3024.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381201
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.b1', 'complements': ['4.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['432.a1.b1', '1008.a1.b1', '1008.b1.b1', '1512.a1.a1', '1512.b1.b1', '1512.c1.b1'], 'contains': ['6048.a1.a1', '6048.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8036, 1903, 6993, 3264, 3909, 7597, 4349, 8214], 'generators': [5, 16], 'label': '12096.r.3024.a1.b1', 'mobius_quo': 0, 'mobius_sub': -504, 'normal_closure': '3024.a1.b1', 'normal_contained_in': ['6.a1.b1', '1512.a1.a1'], 'normal_contains': ['6048.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3024.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1512.779', 'quotient_action_kernel_order': 1512, 'quotient_fusion': None, 'short_label': '3024.a1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381202
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1.a1', 'complements': ['4.b1.b1', '4.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['432.d1.a1', '1008.g1.a1', '1008.i1.a1', '1512.a1.a1', '1512.e1.a1', '1512.h1.a1'], 'contains': ['6048.a1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8757, 3456, 8397, 4957, 5387, 6494, 5189, 5891], 'generators': [16, 9], 'label': '12096.r.3024.b1.a1', 'mobius_quo': 0, 'mobius_sub': -504, 'normal_closure': '3024.b1.a1', 'normal_contained_in': ['6.b1.a1', '1512.a1.a1'], 'normal_contains': ['6048.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3024.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1512.779', 'quotient_action_kernel_order': 1512, 'quotient_fusion': None, 'short_label': '3024.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381203
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '63.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '1008.c1.a1', '1008.d1.a1', '1512.b1.a1', '1512.b1.b1', '1512.d1.a1', '1512.d1.b1', '1512.e1.a1', '1512.f1.a1', '1512.g1.a1'], 'contains': ['6048.a1.a1', '6048.c1.a1', '6048.d1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6583, -1, 7466, -1, 3476, -1, 3814, -1], 'generators': [3604255920, 16], 'label': '12096.r.3024.c1.a1', 'mobius_quo': None, 'mobius_sub': -16, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '3024.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381204
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '1008.e1.a1', '1008.f1.a1', '1512.b1.b1', '1512.c1.a1', '1512.d1.a1', '1512.h1.a1', '1512.i1.a1', '1512.i1.a2'], 'contains': ['6048.a1.a1', '6048.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7919, -1, 7192, -1, 3809, -1, 4281, -1], 'generators': [3604255925, 16], 'label': '12096.r.3024.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '3024.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381205
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.b1', '1008.e1.b1', '1008.f1.b1', '1512.b1.a1', '1512.c1.b1', '1512.d1.b1', '1512.h1.a1', '1512.i1.a1', '1512.i1.a2'], 'contains': ['6048.a1.a1', '6048.e1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7919, -1, 7130, -1, 3809, -1, 4544, -1], 'generators': [16, 3604255927], 'label': '12096.r.3024.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '3024.d1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381206
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.e1.a1', '1008.h1.a1', '1008.j1.a1', '1512.c1.a1', '1512.c1.b1', '1512.e1.a1', '1512.f1.a1', '1512.i1.a1', '1512.i1.a2'], 'contains': ['6048.a1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [8463, -1, 8670, -1, 4708, -1, 4924, -1], 'generators': [3604255929, 16], 'label': '12096.r.3024.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '3024.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381207
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '56.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '28.a1.a1'], 'contains': ['112.a1.b1', '112.b1.a1', '112.c1.a1', '112.f1.b1', '112.g1.b1', '168.a1.b1', '168.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [2483, -1, 2940, -1, 8202, -1, 8115, -1], 'generators': [1604388960, 763233965, 3844124774, 5, 16, 1681587360], 'label': '12096.r.56.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.a1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381208
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.f1.a1', '1008.k1.a1', '1008.l1.a1', '1512.b1.a1', '1512.j1.a1', '1512.k1.a1'], 'contains': ['6048.b1.a1', '6048.c1.a1', '6048.e1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4244, -1, 4780, -1, 2380, -1, 3183, -1], 'generators': [3604255920, 7], 'label': '12096.r.3024.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '3024.f1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381209
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.f1.b1', '1008.k1.b1', '1008.l1.b1', '1512.b1.b1', '1512.j1.b1', '1512.k1.b1'], 'contains': ['6048.b1.b1', '6048.c1.a1', '6048.e1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4244, -1, 5897, -1, 2380, -1, 1996, -1], 'generators': [3604255925, 5], 'label': '12096.r.3024.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '3024.f1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381210
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.g1.a1', '1008.m1.a1', '1008.n1.a1', '1512.b1.a1', '1512.j1.a1'], 'contains': ['6048.b1.a1', '6048.d1.a1', '6048.e1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4923, -1, 4859, -1, 2745, -1, 3427, -1], 'generators': [3604255936, 7], 'label': '12096.r.3024.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '3024.g1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381211
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.g1.b1', '1008.m1.b1', '1008.n1.b1', '1512.b1.b1', '1512.j1.b1'], 'contains': ['6048.b1.b1', '6048.d1.a1', '6048.e1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4923, -1, 6538, -1, 2745, -1, 2548, -1], 'generators': [5, 3604255934], 'label': '12096.r.3024.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '3024.g1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.g1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381212
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '189.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1512.g1.a1', '1512.j1.a1', '1512.j1.b1', '1512.l1.a1', '1512.l1.b1', '1512.m1.a1'], 'contains': ['6048.c1.a1', '6048.d1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 189, 'diagramx': [5997, -1, 7405, -1, 1628, -1, 2277, -1], 'generators': [3604255936, 1574910000], 'label': '12096.r.3024.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '189.a1.a1', 'old_label': '3024.h1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381213
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1512.d1.a1', '1512.j1.b1', '1512.k1.b1', '1512.l1.a1', '1512.n1.a1'], 'contains': ['6048.c1.a1', '6048.e1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [5859, -1, 7281, -1, 1498, -1, 1798, -1], 'generators': [3604255925, 1574910005], 'label': '12096.r.3024.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '378.b1.b1', 'old_label': '3024.i1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381214
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1512.d1.b1', '1512.j1.a1', '1512.k1.a1', '1512.l1.b1', '1512.n1.b1'], 'contains': ['6048.c1.a1', '6048.e1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [5859, -1, 6717, -1, 1498, -1, 2677, -1], 'generators': [1574910000, 3604255927], 'label': '12096.r.3024.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '378.b1.a1', 'old_label': '3024.i1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381215
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '189.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1008.o1.a1', '1512.g1.a1', '1512.k1.a1', '1512.k1.b1', '1512.m1.a1', '1512.n1.a1', '1512.n1.b1', '1512.o1.a1'], 'contains': ['6048.c1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [5588, -1, 6477, -1, 923, -1, 1459, -1], 'generators': [1574910000, 3604255920], 'label': '12096.r.3024.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '3024.j1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.j1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 61381216
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1512.d1.a1', '1512.j1.b1', '1512.l1.a1'], 'contains': ['6048.d1.a1', '6048.e1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [6310, -1, 8454, -1, 2280, -1, 2346, -1], 'generators': [1574910005, 3604255934], 'label': '12096.r.3024.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '378.b1.b1', 'old_label': '3024.k1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381217
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '3024.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '378.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1512.d1.b1', '1512.j1.a1', '1512.l1.b1'], 'contains': ['6048.d1.a1', '6048.e1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 378, 'diagramx': [6310, -1, 7343, -1, 2280, -1, 2985, -1], 'generators': [1574910016, 3604255927], 'label': '12096.r.3024.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '378.b1.a1', 'old_label': '3024.k1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3024.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381218
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['112.a1.a1', '112.c1.a1', '112.e1.a1', '168.c1.a1', '168.d1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3406, -1, 2111, -1, 8836, -1, 8946, -1], 'generators': [3844124776, 1604388978, 7, 16, 1681587360, 763233983], 'label': '12096.r.56.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.111'}
  • id: 61381219
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '4032.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '56.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1344.a1.a1', '1344.b1.a1', '1344.c1.a1', '2016.a1.a1', '2016.c1.a1', '2016.c1.b1', '2016.f1.a1', '2016.h1.a1', '2016.j1.a1', '2016.j1.b1'], 'contains': ['12096.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1192, -1, 2244, -1, 6783, -1, 7041, -1], 'generators': [2087786160], 'label': '12096.r.4032.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '4032.a1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 61381220
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '4032.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '84.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['576.a1.a1', '1008.o1.a1', '1344.a1.a1', '2016.b1.a1', '2016.d1.a1', '2016.d1.b1', '2016.e1.a1', '2016.g1.a1', '2016.i1.a1', '2016.i1.b1'], 'contains': ['12096.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4494, -1, 5453, -1, 2386, -1, 2580, -1], 'generators': [2202727080], 'label': '12096.r.4032.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '4032.b1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4032.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381221
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '6048.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['864.a1.a1', '2016.a1.a1', '2016.b1.a1', '3024.a1.a1', '3024.a1.b1', '3024.b1.a1', '3024.c1.a1', '3024.d1.a1', '3024.d1.b1', '3024.e1.a1'], 'contains': ['12096.a1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7919, 3995, 7077, 4957, 3809, 6087, 4349, 5891], 'generators': [16], 'label': '12096.r.6048.a1.a1', 'mobius_quo': -1, 'mobius_sub': 1008, 'normal_closure': '6048.a1.a1', 'normal_contained_in': ['12.a1.a1', '3024.a1.a1', '3024.a1.b1', '3024.b1.a1'], 'normal_contains': ['12096.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6048.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': '1.1', 'quotient_action_kernel': '10000.dk', 'quotient_action_kernel_order': 6048, 'quotient_fusion': None, 'short_label': '6048.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381222
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '6048.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.b1.a1', '2016.c1.a1', '2016.d1.a1', '3024.a1.a1', '3024.f1.a1', '3024.g1.a1'], 'contains': ['12096.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4200, -1, 4751, -1, 2650, -1, 3363, -1], 'generators': [7], 'label': '12096.r.6048.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3024.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6048.b1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6048.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381223
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '6048.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.b1.b1', '2016.c1.b1', '2016.d1.b1', '3024.a1.b1', '3024.f1.b1', '3024.g1.b1'], 'contains': ['12096.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4200, -1, 5568, -1, 2650, -1, 2520, -1], 'generators': [5], 'label': '12096.r.6048.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3024.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '6048.b1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6048.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381224
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '6048.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '63.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.c1.a1', '2016.e1.a1', '2016.f1.a1', '3024.c1.a1', '3024.f1.a1', '3024.f1.b1', '3024.h1.a1', '3024.i1.a1', '3024.i1.b1', '3024.j1.a1'], 'contains': ['12096.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [4558, -1, 5897, -1, 2185, -1, 2277, -1], 'generators': [3604255920], 'label': '12096.r.6048.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '6048.c1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6048.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381225
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '6048.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '63.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.d1.a1', '2016.g1.a1', '2016.h1.a1', '3024.c1.a1', '3024.g1.a1', '3024.g1.b1', '3024.h1.a1', '3024.k1.a1', '3024.k1.b1'], 'contains': ['12096.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [5239, -1, 6334, -1, 2562, -1, 2640, -1], 'generators': [3604255936], 'label': '12096.r.6048.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '6048.d1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6048.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381226
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '6048.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.e1.a1', '2016.i1.a1', '2016.j1.a1', '3024.d1.a1', '3024.f1.b1', '3024.g1.b1', '3024.i1.a1', '3024.k1.a1'], 'contains': ['12096.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4742, -1, 6088, -1, 2474, -1, 2410, -1], 'generators': [3604255925], 'label': '12096.r.6048.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.b1', 'old_label': '6048.e1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6048.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381227
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '6048.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '126.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['864.e1.b1', '2016.i1.b1', '2016.j1.b1', '3024.d1.b1', '3024.f1.a1', '3024.g1.a1', '3024.i1.b1', '3024.k1.b1'], 'contains': ['12096.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 126, 'diagramx': [4742, -1, 4923, -1, 2474, -1, 3183, -1], 'generators': [3604255927], 'label': '12096.r.6048.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '126.b1.a1', 'old_label': '6048.e1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6048.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381228
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '12096.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': ['1728.a1.a1', '4032.a1.a1', '4032.b1.a1', '6048.a1.a1', '6048.b1.a1', '6048.b1.b1', '6048.c1.a1', '6048.d1.a1', '6048.e1.a1', '6048.e1.b1'], 'contains': [], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4527, 4632, 5547, 5607, 2518, 5141, 2610, 5178], 'generators': [], 'label': '12096.r.12096.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '12096.a1.a1', 'normal_contained_in': ['24.a1.a1', '6048.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '12096.a1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12096.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 61381229
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['112.a1.b1', '112.c1.b1', '112.e1.a1', '168.c1.b1', '168.d1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [3406, -1, 1449, -1, 8836, -1, 8643, -1], 'generators': [1604388978, 763233965, 3844124774, 5, 16, 1681587360], 'label': '12096.r.56.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1.b1', 'subgroup_fusion': None, 'weyl_group': '216.111'}
  • id: 61381230
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['112.a1.a1', '112.a1.b1', '112.d1.a1', '168.e1.a1', '168.f1.a1', '168.g1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3903, -1, 904, -1, 9428, -1, 9440, -1], 'generators': [3844124774, 5, 16, 1681587360, 763233983, 9], 'label': '12096.r.56.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.48'}
  • id: 61381231
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '28.a1.a1'], 'contains': ['112.b1.a1', '112.d1.a1', '112.e1.a1', '168.h1.a1', '168.i1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4545, -1, 3849, -1, 9063, -1, 9101, -1], 'generators': [3844124776, 1604388978, 16, 1681587360, 763233969, 9], 'label': '12096.r.56.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381232
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['112.c1.a1', '112.c1.b1', '112.d1.a1', '168.j1.a1', '168.k1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3663, -1, 2472, -1, 8424, -1, 8779, -1], 'generators': [3844124776, 1604388967, 16, 1681587360, 763233969, 9], 'label': '12096.r.56.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '56.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.111'}
  • id: 61381233
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '63.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['126.a1.a1', '126.a1.b1', '126.b1.a1', '126.b1.b1', '126.c1.a1', '126.d1.a1', '126.e1.a1', '189.a1.a1', '252.b1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7868, -1, 8480, -1, 3374, -1, 4084, -1], 'generators': [3974076847, 2202727103, 1727355725, 5, 16, 1158358447, 9], 'label': '12096.r.63.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '63.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '63.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 61381234
    {'ambient': '12096.r', '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': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '36.a1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.c1.b1', '144.f1.a1', '144.g1.a1', '216.a1.a1', '504.a1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5993, -1, 5270, -1, 2561, -1, 2929, -1], 'generators': [204791760, 125319743, 7, 16, 1038009000], 'label': '12096.r.72.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381235
    {'ambient': '12096.r', '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': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '36.a1.a1'], 'contains': ['144.a1.b1', '144.b1.a1', '144.c1.a1', '144.f1.b1', '144.g1.b1', '216.a1.b1', '504.a1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5993, -1, 5996, -1, 2561, -1, 2176, -1], 'generators': [125319736, 1038009005, 204791765, 5, 16], 'label': '12096.r.72.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.b1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381236
    {'ambient': '12096.r', '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': '3024.b1.a1', 'complements': ['6048.e1.a1', '6048.e1.b1', '6048.b1.a1', '6048.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.a1', '18.b1.a1', '56.d1.a1', '72.d1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7974, 7901, 6703, 8120, 3555, 1517, 4089, 1127], 'generators': [1097123049, 2203575138, 16, 9], 'label': '12096.r.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '10000.dk', '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': '4000.ci'}
  • id: 61381237
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1'], 'contains': ['144.a1.a1', '144.c1.a1', '144.e1.a1', '216.b1.a1', '504.c1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9704, -1, 7020, -1, 3447, -1, 3690, -1], 'generators': [204791760, 125319743, 1038009005, 7, 16], 'label': '12096.r.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '168.47'}
  • id: 61381238
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1'], 'contains': ['144.a1.b1', '144.c1.b1', '144.e1.a1', '216.b1.b1', '504.c1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9704, -1, 7639, -1, 3447, -1, 3381, -1], 'generators': [125319736, 1038009007, 204791765, 5, 16], 'label': '12096.r.72.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.b1', 'subgroup_fusion': None, 'weyl_group': '168.47'}
  • id: 61381239
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '36.a1.a1'], 'contains': ['144.a1.a1', '144.a1.b1', '144.d1.a1', '216.c1.a1', '504.f1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9165, -1, 7826, -1, 4237, -1, 3807, -1], 'generators': [2202727103, 1442090280, 5, 16, 9], 'label': '12096.r.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '168.47'}
  • id: 61381240
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '36.a1.a1'], 'contains': ['144.b1.a1', '144.d1.a1', '144.e1.a1', '216.d1.a1', '504.g1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8690, -1, 7175, -1, 3739, -1, 3965, -1], 'generators': [125319729, 204791760, 16, 1038009000, 9], 'label': '12096.r.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381241
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1'], 'contains': ['144.c1.a1', '144.c1.b1', '144.d1.a1', '216.e1.a1', '504.j1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9956, -1, 6926, -1, 4062, -1, 3593, -1], 'generators': [125319729, 204791760, 1038009005, 16, 9], 'label': '12096.r.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '168.47'}
  • id: 61381242
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '36.b1.a1', '36.c1.a1', '36.c1.b1'], 'contains': ['216.f1.a1', '504.o1.a1', '576.a1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1648, -1, 4740, -1, 242, -1, 405, -1], 'generators': [1158358440, 1727355720, 1442090280, 3974076840, 2202727080], 'label': '12096.r.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 61381243
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '84.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.a1.a1'], 'contains': ['168.a1.a1', '168.a1.b1', '168.c1.a1', '168.c1.b1', '168.e1.a1', '168.h1.a1', '168.j1.a1', '252.b1.a1', '252.c1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4713, -1, 2671, -1, 6994, -1, 6983, -1], 'generators': [1604388978, 3844124774, 5, 16, 763233983, 9], 'label': '12096.r.84.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '84.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61381244
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '84.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '28.a1.a1'], 'contains': ['168.b1.a1', '168.b1.b1', '168.d1.a1', '168.d1.b1', '168.f1.a1', '168.i1.a1', '168.k1.a1', '252.c1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4068, -1, 3379, -1, 8581, -1, 9228, -1], 'generators': [696851407, 2087786169, 5, 16, 2933254814, 9], 'label': '12096.r.84.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '84.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.111'}
  • id: 61381245
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '36.a1.a1'], 'contains': ['216.a1.a1', '216.a1.b1', '216.b1.a1', '216.b1.b1', '216.c1.a1', '216.d1.a1', '216.e1.a1', '756.c1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8790, -1, 6687, -1, 3905, -1, 3486, -1], 'generators': [1099567578, 999821658, 5, 16, 9], 'label': '12096.r.108.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '168.47'}
  • id: 61381246
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '36.b1.a1', '54.a1.a1', '54.a1.b1', '54.b1.a1'], 'contains': ['216.f1.a1', '756.i1.a1', '864.a1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6619, -1, 5771, -1, 939, -1, 1278, -1], 'generators': [1574910000, 3604255920, 16, 3129567856, 2453431680], 'label': '12096.r.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 61381247
    {'ambient': '12096.r', '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': '6048.a1.a1', 'complements': ['4032.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.a1.b1', '6.b1.a1', '27.a1.a1', '84.b1.a1', '108.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7705, 1300, 5885, 2657, 3813, 7833, 3738, 8458], 'generators': [3017352983, 5, 16, 2977159703, 9], 'label': '12096.r.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.a1.b1', '6.b1.a1', '1512.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10000.dk'}
  • id: 61381248
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '36.c1.a1', '54.a1.a1'], 'contains': ['216.f1.a1', '756.k1.a1', '864.b1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1467, -1, 4383, -1, 582, -1, 1005, -1], 'generators': [2453431687, 1574910000, 3604255920, 3129567847, 7], 'label': '12096.r.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 61381249
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '36.c1.b1', '54.a1.b1'], 'contains': ['216.f1.a1', '756.k1.b1', '864.b1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1467, -1, 5404, -1, 582, -1, 275, -1], 'generators': [3604255925, 1574910005, 2453431685, 5, 3129567845], 'label': '12096.r.108.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '108.c1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.b1', 'subgroup_fusion': None, 'weyl_group': '168.43'}
  • id: 61381250
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '56.b1.a1', '56.c1.a1'], 'contains': ['224.a1.a1', '224.b1.a1', '336.a1.a1', '336.b1.a1', '336.c1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3161, -1, 808, -1, 9210, -1, 9440, -1], 'generators': [3844124776, 7, 16, 1681587360, 763233983], 'label': '12096.r.112.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 61381251
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.b1', '56.b1.b1', '56.c1.a1'], 'contains': ['224.a1.a1', '224.b1.b1', '336.a1.b1', '336.b1.b1', '336.c1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [3161, -1, 666, -1, 9210, -1, 8680, -1], 'generators': [763233965, 3844124774, 5, 16, 1681587360], 'label': '12096.r.112.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.a1.b1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 61381252
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '56.a1.a1', '56.a1.b1', '56.d1.a1'], 'contains': ['224.a1.a1', '224.c1.a1', '224.d1.a1', '336.d1.a1', '336.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2264, -1, 3712, -1, 7998, -1, 8251, -1], 'generators': [3844124776, 1604388960, 763233976, 16, 1681587360], 'label': '12096.r.112.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381253
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.b1', '56.b1.a1', '56.e1.a1'], 'contains': ['224.a1.a1', '224.e1.a1', '336.f1.a1', '336.g1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2904, -1, 2216, -1, 8601, -1, 8391, -1], 'generators': [3844124776, 1604388974, 763233976, 16, 1681587360], 'label': '12096.r.112.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381254
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '56.b1.b1', '56.e1.a1'], 'contains': ['224.a1.a1', '224.e1.b1', '336.f1.b1', '336.g1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [2904, -1, 1401, -1, 8601, -1, 8829, -1], 'generators': [3844124776, 1604388967, 763233976, 16, 1681587360], 'label': '12096.r.112.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.c1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381255
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '56.d1.a1', '56.e1.a1'], 'contains': ['224.a1.a1', '336.h1.a1', '336.j1.a1', '336.k1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3753, -1, 1555, -1, 9741, -1, 9704, -1], 'generators': [3844124776, 16, 1681587360, 763233969, 9], 'label': '12096.r.112.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 61381256
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1', '56.b1.b1', '56.d1.a1'], 'contains': ['224.a1.a1', '336.i1.a1', '336.l1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4420, -1, 1294, -1, 9398, -1, 9082, -1], 'generators': [3844124776, 1604388978, 763233976, 16, 1681587360], 'label': '12096.r.112.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '112.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381257
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '56.a1.a1'], 'contains': ['224.b1.a1', '224.c1.a1', '224.e1.b1', '336.m1.a1', '336.n1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [575, -1, 2397, -1, 7748, -1, 7948, -1], 'generators': [1604388967, 3844124760, 7, 763233967, 1681587360], 'label': '12096.r.112.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '112.f1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381258
    {'ambient': '12096.r', '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': '1512.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '36.b1.a1', '112.b1.a1', '144.b1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5527, 7901, 5275, 6586, 2242, 1517, 2122, 1362], 'generators': [2203575120, 1097123056, 16], 'label': '12096.r.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1512.779'}
  • id: 61381259
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '56.a1.b1'], 'contains': ['224.b1.b1', '224.c1.a1', '224.e1.a1', '336.m1.b1', '336.n1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [575, -1, 3187, -1, 7748, -1, 7637, -1], 'generators': [1604388960, 14, 3844124774, 1681587360, 763233974], 'label': '12096.r.112.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '112.f1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381260
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1'], 'contains': ['224.b1.a1', '224.d1.a1', '224.e1.b1', '336.o1.a1', '336.p1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [969, -1, 971, -1, 8202, -1, 8531, -1], 'generators': [3844124760, 1604388983, 7, 763233967, 1681587360], 'label': '12096.r.112.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.a1', 'old_label': '112.g1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381261
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.b1'], 'contains': ['224.b1.b1', '224.d1.a1', '224.e1.a1', '336.o1.b1', '336.p1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [969, -1, 2693, -1, 8202, -1, 7777, -1], 'generators': [1604388976, 14, 3844124774, 1681587360, 763233974], 'label': '12096.r.112.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.a1.b1', 'old_label': '112.g1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 61381262
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '126.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['63.a1.a1'], 'contains': ['252.a1.a1', '252.d1.a1', '252.f1.a1', '378.a1.a1', '504.c1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7317, -1, 9301, -1, 3009, -1, 4445, -1], 'generators': [2202727103, 1727355720, 7, 16, 1158358447, 3974076858], 'label': '12096.r.126.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '126.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 61381263
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '126.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['63.a1.a1'], 'contains': ['252.a1.b1', '252.d1.b1', '252.f1.a1', '378.a1.b1', '504.c1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 63, 'diagramx': [7317, -1, 8530, -1, 3009, -1, 4331, -1], 'generators': [3974076847, 1158358454, 1727355725, 5, 16, 2202727085], 'label': '12096.r.126.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '126.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.a1.b1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 61381264
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '126.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '63.a1.a1'], 'contains': ['252.a1.a1', '252.d1.b1', '252.g1.a1', '252.h1.a1', '252.i1.a1', '378.b1.a1', '504.a1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [6742, -1, 6324, -1, 1885, -1, 2291, -1], 'generators': [3974076847, 2202727103, 1727355720, 7, 16, 1158358447], 'label': '12096.r.126.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '126.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61381265
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '126.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '63.a1.a1'], 'contains': ['252.a1.b1', '252.d1.a1', '252.g1.a1', '252.h1.b1', '252.i1.b1', '378.b1.b1', '504.a1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 63, 'diagramx': [6742, -1, 7453, -1, 1885, -1, 1978, -1], 'generators': [3974076854, 1158358454, 1727355725, 5, 16, 2202727085], 'label': '12096.r.126.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '126.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61381266
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '126.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['63.a1.a1'], 'contains': ['252.a1.a1', '252.a1.b1', '252.e1.a1', '378.c1.a1', '504.f1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [8034, -1, 9063, -1, 4722, -1, 4848, -1], 'generators': [2202727103, 1727355725, 5, 16, 1158358447, 9], 'label': '12096.r.126.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '126.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 61381267
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '126.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['63.a1.a1'], 'contains': ['252.d1.a1', '252.d1.b1', '252.e1.a1', '378.d1.a1', '504.j1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [8196, -1, 8428, -1, 4528, -1, 4559, -1], 'generators': [2202727089, 3974076847, 1727355720, 16, 1158358458, 9], 'label': '12096.r.126.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '126.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.d1.a1', 'subgroup_fusion': None, 'weyl_group': '48.49'}
  • id: 61381268
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '126.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '63.a1.a1'], 'contains': ['252.e1.a1', '252.f1.a1', '252.g1.a1', '378.e1.a1', '504.g1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 63, 'diagramx': [7828, -1, 8660, -1, 3461, -1, 4703, -1], 'generators': [2202727089, 1727355720, 16, 3974076858, 1158358458, 9], 'label': '12096.r.126.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '63.a1.a1', 'old_label': '126.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '126.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.13'}
  • id: 61381269
    {'ambient': '12096.r', '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': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.b1.a1', '36.c1.a1', '112.f1.a1', '144.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1599, -1, 4074, -1, 1552, -1, 1714, -1], 'generators': [2203575127, 7, 1097123047], 'label': '12096.r.4.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1512.779'}
  • id: 61381270
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '72.a1.a1', '72.b1.a1', '72.c1.a1'], 'contains': ['288.a1.a1', '288.b1.a1', '432.a1.a1', '1008.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9119, -1, 5838, -1, 2726, -1, 3105, -1], 'generators': [2202727103, 1442090280, 7, 16], 'label': '12096.r.144.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381271
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '72.a1.b1', '72.b1.b1', '72.c1.a1'], 'contains': ['288.a1.a1', '288.b1.b1', '432.a1.b1', '1008.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9119, -1, 7212, -1, 2726, -1, 2142, -1], 'generators': [1442090280, 5, 16, 2202727085], 'label': '12096.r.144.a1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.b1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381272
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1512.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '72.a1.a1', '72.a1.b1', '72.d1.a1'], 'contains': ['288.a1.a1', '288.c1.a1', '288.d1.a1', '432.b1.a1', '1008.c1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5982, -1, 5296, -1, 2242, -1, 2006, -1], 'generators': [204791760, 125319736, 16, 1038009000], 'label': '12096.r.144.b1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381273
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.b1', '72.b1.a1', '72.e1.a1'], 'contains': ['288.a1.a1', '288.e1.a1', '432.c1.a1', '1008.e1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9878, -1, 7090, -1, 3117, -1, 2824, -1], 'generators': [204791760, 125319736, 1038009005, 16], 'label': '12096.r.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381274
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.b1', '72.e1.a1'], 'contains': ['288.a1.a1', '288.e1.b1', '432.c1.b1', '1008.e1.b1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9878, -1, 6890, -1, 3117, -1, 2937, -1], 'generators': [204791760, 125319736, 1038009007, 16], 'label': '12096.r.144.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.c1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.b1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381275
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1'], 'contains': ['288.a1.a1', '432.d1.a1', '1008.i1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9466, -1, 7834, -1, 4049, -1, 4153, -1], 'generators': [2202727089, 1442090280, 16, 9], 'label': '12096.r.144.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381276
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.b1.b1', '72.d1.a1'], 'contains': ['288.a1.a1', '432.e1.a1', '1008.j1.a1'], 'core': '6048.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9636, -1, 7614, -1, 3512, -1, 3804, -1], 'generators': [204791760, 125319736, 16, 1038009009], 'label': '12096.r.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381277
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '72.a1.a1'], 'contains': ['288.b1.a1', '288.c1.a1', '288.e1.b1', '432.f1.a1', '1008.k1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2380, -1, 4378, -1, 1530, -1, 1274, -1], 'generators': [23, 204791760, 125319743, 1038009000], 'label': '12096.r.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '144.f1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381278
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '72.a1.b1'], 'contains': ['288.b1.b1', '288.c1.a1', '288.e1.a1', '432.f1.b1', '1008.k1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [2380, -1, 5181, -1, 1530, -1, 110, -1], 'generators': [125319720, 1038009005, 204791765, 5], 'label': '12096.r.144.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.b1', 'old_label': '144.f1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381279
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1'], 'contains': ['288.b1.a1', '288.d1.a1', '288.e1.b1', '432.g1.a1', '1008.m1.a1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5123, -1, 4807, -1, 1696, -1, 1387, -1], 'generators': [204791760, 125319727, 1038009016, 7], 'label': '12096.r.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.a1', 'old_label': '144.g1.a1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381280
    {'ambient': '12096.r', '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': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1'], 'contains': ['8.a1.a1', '12.b1.b1', '36.c1.b1', '112.f1.b1', '144.f1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1599, -1, 4930, -1, 1552, -1, 639, -1], 'generators': [5, 2203575125, 1097123040], 'label': '12096.r.4.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '4.b1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1512.779'}
  • id: 61381281
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.b1'], 'contains': ['288.b1.b1', '288.d1.a1', '288.e1.a1', '432.g1.b1', '1008.m1.b1'], 'core': '12096.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5123, -1, 5687, -1, 1696, -1, 405, -1], 'generators': [125319720, 204791765, 5, 1038009014], 'label': '12096.r.144.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.a1.b1', 'old_label': '144.g1.b1', 'projective_image': '12096.r', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.b1', 'subgroup_fusion': None, 'weyl_group': '42.1'}
  • id: 61381282
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.a1', '84.a1.a1'], 'contains': ['336.a1.a1', '336.d1.a1', '336.f1.b1', '336.m1.a1', '336.o1.a1', '504.a1.a1', '504.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [2485, -1, 1772, -1, 6460, -1, 6617, -1], 'generators': [3844124776, 1604388967, 7, 16, 763233983], 'label': '12096.r.168.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '168.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381283
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1.b1', '84.a1.a1'], 'contains': ['336.a1.b1', '336.d1.a1', '336.f1.a1', '336.m1.b1', '336.o1.b1', '504.a1.b1', '504.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [2485, -1, 3083, -1, 6460, -1, 6441, -1], 'generators': [1604388960, 763233965, 3844124774, 5, 16], 'label': '12096.r.168.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '168.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.a1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381284
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '56.a1.a1', '84.b1.a1'], 'contains': ['336.b1.a1', '336.e1.a1', '336.g1.b1', '336.n1.a1', '336.p1.a1', '504.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [1877, -1, 3407, -1, 8402, -1, 8965, -1], 'generators': [696851407, 2087786183, 7, 16, 2933254816], 'label': '12096.r.168.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '168.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381285
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '56.a1.b1', '84.b1.a1'], 'contains': ['336.b1.b1', '336.e1.a1', '336.g1.a1', '336.n1.b1', '336.p1.b1', '504.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [1877, -1, 3664, -1, 8402, -1, 8115, -1], 'generators': [696851414, 2087786176, 5, 16, 2933254814], 'label': '12096.r.168.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '168.b1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.b1.b1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381286
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1', '84.a1.a1'], 'contains': ['336.a1.a1', '336.f1.a1', '336.i1.a1', '504.c1.a1', '504.d1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4082, -1, 2034, -1, 6692, -1, 7052, -1], 'generators': [3844124776, 1604388978, 7, 16, 763233983], 'label': '12096.r.168.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '168.c1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61381287
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.b1', '84.a1.a1'], 'contains': ['336.a1.b1', '336.f1.b1', '336.i1.a1', '504.c1.b1', '504.d1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 84, 'diagramx': [4082, -1, 1380, -1, 6692, -1, 6775, -1], 'generators': [1604388978, 763233965, 3844124774, 5, 16], 'label': '12096.r.168.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '168.c1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61381288
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.a1', '84.b1.a1'], 'contains': ['336.b1.a1', '336.g1.a1', '336.l1.a1', '504.d1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3374, -1, 2426, -1, 8869, -1, 9323, -1], 'generators': [696851407, 2087786183, 7, 16, 2933254814], 'label': '12096.r.168.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '168.d1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.a1', 'subgroup_fusion': None, 'weyl_group': '216.111'}
  • id: 61381289
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.b1.b1', '84.b1.a1'], 'contains': ['336.b1.b1', '336.g1.b1', '336.l1.a1', '504.d1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 28, 'diagramx': [3374, -1, 2131, -1, 8869, -1, 9170, -1], 'generators': [696851414, 2087786176, 2933254823, 5, 16], 'label': '12096.r.168.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '168.d1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1.b1', 'subgroup_fusion': None, 'weyl_group': '216.111'}
  • id: 61381290
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '84.a1.a1'], 'contains': ['336.a1.a1', '336.a1.b1', '336.h1.a1', '504.e1.a1', '504.f1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [4770, -1, 1208, -1, 7290, -1, 7325, -1], 'generators': [3844124774, 5, 16, 763233983, 9], 'label': '12096.r.168.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '168.e1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61381291
    {'ambient': '12096.r', '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': '3024.a1.a1', 'complements': ['2016.i1.a1', '2016.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '54.a1.a1', '168.b1.a1', '216.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2877, 1806, 5083, 4137, 2540, 7597, 2553, 5881], 'generators': [3017352983, 7, 16, 2977159703], 'label': '12096.r.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', '3024.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4000.ci'}
  • id: 61381292
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1', '84.b1.a1'], 'contains': ['336.b1.a1', '336.b1.b1', '336.j1.a1', '504.e1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3900, -1, 1559, -1, 9555, -1, 9831, -1], 'generators': [696851407, 2087786169, 5, 16, 9], 'label': '12096.r.168.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '168.f1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.15'}
  • id: 61381293
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '672.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.c1.a1'], 'contains': ['336.c1.a1', '336.c1.b1', '336.k1.a1', '504.e1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4262, -1, 253, -1, 9927, -1, 9946, -1], 'generators': [3844124774, 5, 16, 1681587360, 9], 'label': '12096.r.168.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '56.c1.a1', 'old_label': '168.g1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 61381294
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1008.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.d1.a1', '84.a1.a1'], 'contains': ['336.d1.a1', '336.h1.a1', '336.i1.a1', '504.g1.a1', '504.h1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [5529, -1, 3836, -1, 6894, -1, 7190, -1], 'generators': [3844124776, 1604388978, 16, 763233969, 9], 'label': '12096.r.168.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '168.h1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 61381295
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '56.d1.a1', '84.b1.a1'], 'contains': ['336.e1.a1', '336.j1.a1', '336.l1.a1', '504.h1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [5350, -1, 4064, -1, 9010, -1, 9576, -1], 'generators': [696851418, 2087786169, 16, 2933254816, 9], 'label': '12096.r.168.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '168.i1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.i1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 61381296
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2016.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.e1.a1', '84.a1.a1'], 'contains': ['336.f1.a1', '336.f1.b1', '336.h1.a1', '504.j1.a1', '504.k1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [4443, -1, 2788, -1, 7093, -1, 6914, -1], 'generators': [3844124776, 1604388967, 16, 763233969, 9], 'label': '12096.r.168.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '84.a1.a1', 'old_label': '168.j1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.j1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 61381297
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '168.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.e1.a1', '84.b1.a1'], 'contains': ['336.g1.a1', '336.g1.b1', '336.j1.a1', '504.k1.a1'], 'core': '3024.b1.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [3534, -1, 2970, -1, 8758, -1, 9247, -1], 'generators': [696851418, 2087786169, 16, 2933254814, 9], 'label': '12096.r.168.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.a1.a1', 'old_label': '168.k1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.k1.a1', 'subgroup_fusion': None, 'weyl_group': '216.111'}
  • id: 61381298
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '189.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '756.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '63.a1.a1'], 'contains': ['378.a1.a1', '378.a1.b1', '378.b1.a1', '378.b1.b1', '378.c1.a1', '378.d1.a1', '378.e1.a1'], 'core': '1512.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7576, -1, 8873, -1, 3236, -1, 4208, -1], 'generators': [3604255925, 1574910005, 5, 16, 3129567863, 9], 'label': '12096.r.189.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '189.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '189.a1.a1', 'subgroup_fusion': None, 'weyl_group': '84.9'}
  • id: 61381299
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '72.a1.a1', '108.a1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.c1.b1', '432.f1.a1', '432.g1.a1', '1512.b1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5856, -1, 5071, -1, 2422, -1, 2606, -1], 'generators': [999821647, 1099567567, 7, 16], 'label': '12096.r.216.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381300
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3024.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '72.a1.b1', '108.a1.a1'], 'contains': ['432.a1.b1', '432.b1.a1', '432.c1.a1', '432.f1.b1', '432.g1.b1', '1512.b1.b1'], 'core': '3024.a1.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [5856, -1, 6038, -1, 2422, -1, 1883, -1], 'generators': [1099567560, 999821640, 5, 16], 'label': '12096.r.216.a1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.a1.b1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.b1', 'subgroup_fusion': None, 'weyl_group': '84.7'}
  • id: 61381301
    {'ambient': '12096.r', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6048.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '108.a1.a1'], 'contains': ['432.a1.a1', '432.c1.a1', '432.e1.a1', '1512.c1.a1'], 'core': '3024.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [9721, -1, 6764, -1, 3658, -1, 3704, -1], 'generators': [999821658, 1099567567, 7, 16], 'label': '12096.r.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '10000.dk', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '168.47'}