Abstract group data - 5832.gj

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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': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 18, 'aut_gen_orders': [18, 6, 6, 18, 6], 'aut_gens': [[1, 6, 72, 216, 648], [1429, 1626, 2232, 216, 720], [397, 354, 4032, 432, 5112], [4165, 2010, 4176, 432, 3240], [4825, 2922, 504, 216, 2592], [3301, 3318, 4248, 216, 5544]], 'aut_group': None, 'aut_hash': 7751161452078693781, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 34992, 'aut_permdeg': 114, 'aut_perms': [1088599598935982493984803590383029132520398829427440679570357552292625319566799391935392498739058735127085840007244230653296175459706647024771617152452667170797020859257687300615159038800, 527018184521472522180781167581269553684625543819455830343274216305212497350900600989926424473356795024537770007342315614368869714887743466767078965389230789498875486544446266866171860340, 980652715134268016959423464154066993914141447863582068556160245795650776590694252381880758540927641813413487539488424686572414165169160068089969090001949522924173814147537412862552413330, 1885685269028084908138159774096651821325732811445066976409080424785415537090043825549973538595917747550728519938519751650962647607903082481978492541177706480890124774913153978864627522748, 358216505603170232276817126588010955363492565343496013082744061906785179567538407769337499838616391878188190887427299816632140239423263800396248414181722362679440199976369865099323883047], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 81, 2, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 6, 1, 2], [3, 9, 1, 2], [3, 12, 1, 2], [3, 18, 1, 1], [3, 54, 1, 3], [4, 27, 2, 2], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 1, 2], [6, 9, 1, 2], [6, 12, 1, 2], [6, 18, 1, 1], [6, 54, 1, 3], [6, 81, 2, 2], [6, 162, 2, 3], [9, 36, 3, 3], [9, 54, 1, 3], [12, 54, 2, 2], [12, 81, 2, 4], [12, 162, 2, 3], [18, 36, 3, 3], [18, 54, 1, 3], [36, 162, 2, 3]], 'aut_supersolvable': True, 'aut_tex': 'C_3^3.C_3^4.C_2^4', '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': 18, 'autcentquo_group': '8748.nu', 'autcentquo_hash': 226253444510477509, 'autcentquo_nilpotent': False, 'autcentquo_order': 8748, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_3^5.S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 81, 2], [3, 2, 2], [3, 4, 1], [3, 6, 2], [3, 9, 2], [3, 12, 2], [3, 18, 1], [3, 54, 3], [4, 27, 4], [6, 2, 2], [6, 4, 1], [6, 6, 2], [6, 9, 2], [6, 12, 2], [6, 18, 1], [6, 54, 3], [6, 81, 4], [6, 162, 6], [9, 36, 9], [9, 54, 3], [12, 54, 4], [12, 81, 8], [12, 162, 6], [18, 36, 9], [18, 54, 3], [36, 162, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '2916.ef', 'commutator_count': 1, 'commutator_label': '243.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 166, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 81, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [3, 6, 2, 1], [3, 9, 2, 1], [3, 12, 2, 1], [3, 18, 1, 1], [3, 54, 1, 1], [3, 54, 2, 1], [4, 27, 2, 2], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 2, 1], [6, 9, 2, 1], [6, 12, 2, 1], [6, 18, 1, 1], [6, 54, 1, 1], [6, 54, 2, 1], [6, 81, 2, 2], [6, 162, 1, 2], [6, 162, 2, 2], [9, 36, 1, 3], [9, 36, 2, 3], [9, 54, 1, 1], [9, 54, 2, 1], [12, 54, 2, 2], [12, 81, 4, 2], [12, 162, 2, 1], [12, 162, 4, 1], [18, 36, 1, 3], [18, 36, 2, 3], [18, 54, 1, 1], [18, 54, 2, 1], [36, 162, 2, 1], [36, 162, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 36, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 6], [12, 1, 3]], 'familial': False, 'frattini_label': '54.15', 'frattini_quotient': '108.38', 'hash': 5408304993545916615, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 6, 3, 3, 9], 'inner_gens': [[1, 2262, 2232, 432, 5256], [2569, 6, 2520, 216, 3312], [4321, 4254, 72, 216, 1080], [433, 6, 72, 216, 648], [1657, 3606, 288, 216, 648]], 'inner_hash': 7107432785865780292, 'inner_nilpotent': False, 'inner_order': 2916, 'inner_split': True, 'inner_tex': 'C_3^4.S_3^2', 'inner_used': [1, 2, 5], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 24], [2, 24], [4, 6], [6, 12], [12, 18], [18, 8]], 'label': '5832.gj', 'linC_count': 9, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 3, 'linQ_dim': 12, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C3^3*C6).S3^2', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 60, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 92, 'number_divisions': 54, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 410, 'number_subgroup_classes': 553, 'number_subgroups': 11692, 'old_label': None, 'order': 5832, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 163], [3, 242], [4, 108], [6, 1538], [9, 486], [12, 1836], [18, 486], [36, 972]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[4153, 66, 288, 432, 5760], [2533, 30, 144, 432, 2880]], 'outer_group': '12.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [24, 724], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 10], [6, 4], [8, 4], [12, 10], [18, 4], [24, 6], [36, 2]], 'representations': {'PC': {'code': '11432718641802709561391225324569715360439104460029291232792419584899951449930445650937168949709445791', 'gens': [1, 3, 6, 7, 8], 'pres': [9, 2, 3, 2, 2, 3, 3, 3, 3, 3, 18, 61076, 2036, 74, 149907, 74100, 102, 109084, 54013, 120533, 22703, 9104, 8951, 27222, 378439, 108880, 39769, 4354, 8251, 1132, 286, 314936, 52514]}, 'Perm': {'d': 22, 'gens': [53780695250956990689, 56334846222849696609]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_3^3\\times C_6).S_3^2', '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: 164582613
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 166, 'group_order': 5832, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 164582624
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 166, 'group_order': 5832, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 36, 'size': 1}
  • id: 164582635
    {'aut_label': '2B', 'centralizer': '81.a1.a1', 'counter': 3, 'group_counter': 166, 'group_order': 5832, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1071, 'size': 81}
  • id: 164582646
    {'aut_label': '2B', 'centralizer': '81.a1.a1', 'counter': 4, 'group_counter': 166, 'group_order': 5832, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 5043, 'size': 81}
  • id: 164582657
    {'aut_label': '3A', 'centralizer': '2.b1.a1', 'counter': 5, 'group_counter': 166, 'group_order': 5832, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 216, 'size': 2}
  • id: 164582668
    {'aut_label': '3B', 'centralizer': '2.c1.a1', 'counter': 6, 'group_counter': 166, 'group_order': 5832, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 3888, 'size': 2}
  • id: 164582679
    {'aut_label': '3C', 'centralizer': '4.a1.a1', 'counter': 7, 'group_counter': 166, 'group_order': 5832, 'label': '3C', 'order': 3, 'powers': [7, 1], 'representative': 2160, 'size': 4}
  • id: 164582690
    {'aut_label': '3D1', 'centralizer': '6.g1.a1', 'counter': 8, 'group_counter': 166, 'group_order': 5832, 'label': '3D1', 'order': 3, 'powers': [9, 1], 'representative': 4, 'size': 6}
  • id: 164582701
    {'aut_label': '3D-1', 'centralizer': '6.g1.a1', 'counter': 9, 'group_counter': 166, 'group_order': 5832, 'label': '3D-1', 'order': 3, 'powers': [8, 1], 'representative': 2, 'size': 6}
  • id: 164582614
    {'aut_label': '3E1', 'centralizer': '9.a1.a1', 'counter': 10, 'group_counter': 166, 'group_order': 5832, 'label': '3E1', 'order': 3, 'powers': [11, 1], 'representative': 362, 'size': 9}
  • id: 164582615
    {'aut_label': '3E-1', 'centralizer': '9.a1.a1', 'counter': 11, 'group_counter': 166, 'group_order': 5832, 'label': '3E-1', 'order': 3, 'powers': [10, 1], 'representative': 508, 'size': 9}
  • id: 164582616
    {'aut_label': '3F1', 'centralizer': '12.e1.a1', 'counter': 12, 'group_counter': 166, 'group_order': 5832, 'label': '3F1', 'order': 3, 'powers': [13, 1], 'representative': 3892, 'size': 12}
  • id: 164582617
    {'aut_label': '3F-1', 'centralizer': '12.e1.a1', 'counter': 13, 'group_counter': 166, 'group_order': 5832, 'label': '3F-1', 'order': 3, 'powers': [12, 1], 'representative': 1946, 'size': 12}
  • id: 164582618
    {'aut_label': '3G', 'centralizer': '18.c1.a1', 'counter': 14, 'group_counter': 166, 'group_order': 5832, 'label': '3G', 'order': 3, 'powers': [14, 1], 'representative': 144, 'size': 18}
  • id: 164582619
    {'aut_label': '3H', 'centralizer': '54.v1.a1', 'counter': 15, 'group_counter': 166, 'group_order': 5832, 'label': '3H', 'order': 3, 'powers': [15, 1], 'representative': 240, 'size': 54}
  • id: 164582620
    {'aut_label': '3I1', 'centralizer': '54.x1.a1', 'counter': 16, 'group_counter': 166, 'group_order': 5832, 'label': '3I1', 'order': 3, 'powers': [17, 1], 'representative': 1970, 'size': 54}
  • id: 164582621
    {'aut_label': '3I-1', 'centralizer': '54.x1.a1', 'counter': 17, 'group_counter': 166, 'group_order': 5832, 'label': '3I-1', 'order': 3, 'powers': [16, 1], 'representative': 484, 'size': 54}
  • id: 164582622
    {'aut_label': '4A1', 'centralizer': '27.e1.a1', 'counter': 18, 'group_counter': 166, 'group_order': 5832, 'label': '4A1', 'order': 4, 'powers': [2, 19], 'representative': 1134, 'size': 27}
  • id: 164582623
    {'aut_label': '4A1', 'centralizer': '27.e1.a1', 'counter': 19, 'group_counter': 166, 'group_order': 5832, 'label': '4A-1', 'order': 4, 'powers': [2, 18], 'representative': 1098, 'size': 27}
  • id: 164582625
    {'aut_label': '4B1', 'centralizer': '27.f1.a1', 'counter': 20, 'group_counter': 166, 'group_order': 5832, 'label': '4B1', 'order': 4, 'powers': [2, 21], 'representative': 69, 'size': 27}
  • id: 164582626
    {'aut_label': '4B1', 'centralizer': '27.f1.a1', 'counter': 21, 'group_counter': 166, 'group_order': 5832, 'label': '4B-1', 'order': 4, 'powers': [2, 20], 'representative': 33, 'size': 27}
  • id: 164582627
    {'aut_label': '6A', 'centralizer': '2.b1.a1', 'counter': 22, 'group_counter': 166, 'group_order': 5832, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 468, 'size': 2}
  • id: 164582628
    {'aut_label': '6B', 'centralizer': '2.c1.a1', 'counter': 23, 'group_counter': 166, 'group_order': 5832, 'label': '6B', 'order': 6, 'powers': [6, 2], 'representative': 1980, 'size': 2}
  • id: 164582629
    {'aut_label': '6C', 'centralizer': '4.a1.a1', 'counter': 24, 'group_counter': 166, 'group_order': 5832, 'label': '6C', 'order': 6, 'powers': [7, 2], 'representative': 4356, 'size': 4}
  • id: 164582630
    {'aut_label': '6D1', 'centralizer': '6.g1.a1', 'counter': 25, 'group_counter': 166, 'group_order': 5832, 'label': '6D1', 'order': 6, 'powers': [8, 2], 'representative': 38, 'size': 6}
  • id: 164582631
    {'aut_label': '6D-1', 'centralizer': '6.g1.a1', 'counter': 26, 'group_counter': 166, 'group_order': 5832, 'label': '6D-1', 'order': 6, 'powers': [9, 2], 'representative': 40, 'size': 6}
  • id: 164582632
    {'aut_label': '6E1', 'centralizer': '9.a1.a1', 'counter': 27, 'group_counter': 166, 'group_order': 5832, 'label': '6E1', 'order': 6, 'powers': [10, 2], 'representative': 4432, 'size': 9}
  • id: 164582633
    {'aut_label': '6E-1', 'centralizer': '9.a1.a1', 'counter': 28, 'group_counter': 166, 'group_order': 5832, 'label': '6E-1', 'order': 6, 'powers': [11, 2], 'representative': 2342, 'size': 9}
  • id: 164582634
    {'aut_label': '6F1', 'centralizer': '12.e1.a1', 'counter': 29, 'group_counter': 166, 'group_order': 5832, 'label': '6F1', 'order': 6, 'powers': [12, 2], 'representative': 1982, 'size': 12}
  • id: 164582636
    {'aut_label': '6F-1', 'centralizer': '12.e1.a1', 'counter': 30, 'group_counter': 166, 'group_order': 5832, 'label': '6F-1', 'order': 6, 'powers': [13, 2], 'representative': 1984, 'size': 12}
  • id: 164582637
    {'aut_label': '6G', 'centralizer': '18.c1.a1', 'counter': 31, 'group_counter': 166, 'group_order': 5832, 'label': '6G', 'order': 6, 'powers': [14, 2], 'representative': 108, 'size': 18}
  • id: 164582638
    {'aut_label': '6H', 'centralizer': '54.v1.a1', 'counter': 32, 'group_counter': 166, 'group_order': 5832, 'label': '6H', 'order': 6, 'powers': [15, 2], 'representative': 444, 'size': 54}
  • id: 164582639
    {'aut_label': '6I1', 'centralizer': '54.x1.a1', 'counter': 33, 'group_counter': 166, 'group_order': 5832, 'label': '6I1', 'order': 6, 'powers': [16, 2], 'representative': 448, 'size': 54}
  • id: 164582640
    {'aut_label': '6I-1', 'centralizer': '54.x1.a1', 'counter': 34, 'group_counter': 166, 'group_order': 5832, 'label': '6I-1', 'order': 6, 'powers': [17, 2], 'representative': 2006, 'size': 54}
  • id: 164582641
    {'aut_label': '6J1', 'centralizer': '81.a1.a1', 'counter': 35, 'group_counter': 166, 'group_order': 5832, 'label': '6J1', 'order': 6, 'powers': [10, 4], 'representative': 5617, 'size': 81}
  • id: 164582642
    {'aut_label': '6J-1', 'centralizer': '81.a1.a1', 'counter': 36, 'group_counter': 166, 'group_order': 5832, 'label': '6J-1', 'order': 6, 'powers': [11, 4], 'representative': 1589, 'size': 81}
  • id: 164582643
    {'aut_label': '6J-1', 'centralizer': '81.a1.a1', 'counter': 37, 'group_counter': 166, 'group_order': 5832, 'label': '6K1', 'order': 6, 'powers': [11, 3], 'representative': 2969, 'size': 81}
  • id: 164582644
    {'aut_label': '6J1', 'centralizer': '81.a1.a1', 'counter': 38, 'group_counter': 166, 'group_order': 5832, 'label': '6K-1', 'order': 6, 'powers': [10, 3], 'representative': 949, 'size': 81}
  • id: 164582645
    {'aut_label': '6L', 'centralizer': '162.a1.a1', 'counter': 39, 'group_counter': 166, 'group_order': 5832, 'label': '6L', 'order': 6, 'powers': [14, 4], 'representative': 3171, 'size': 162}
  • id: 164582647
    {'aut_label': '6L', 'centralizer': '162.a1.a1', 'counter': 40, 'group_counter': 166, 'group_order': 5832, 'label': '6M', 'order': 6, 'powers': [14, 3], 'representative': 2295, 'size': 162}
  • id: 164582648
    {'aut_label': '6N1', 'centralizer': '162.a1.a1', 'counter': 41, 'group_counter': 166, 'group_order': 5832, 'label': '6N1', 'order': 6, 'powers': [8, 3], 'representative': 2657, 'size': 162}
  • id: 164582649
    {'aut_label': '6N-1', 'centralizer': '162.a1.a1', 'counter': 42, 'group_counter': 166, 'group_order': 5832, 'label': '6N-1', 'order': 6, 'powers': [9, 3], 'representative': 5101, 'size': 162}
  • id: 164582650
    {'aut_label': '6N1', 'centralizer': '162.a1.a1', 'counter': 43, 'group_counter': 166, 'group_order': 5832, 'label': '6O1', 'order': 6, 'powers': [8, 4], 'representative': 1445, 'size': 162}
  • id: 164582651
    {'aut_label': '6N-1', 'centralizer': '162.a1.a1', 'counter': 44, 'group_counter': 166, 'group_order': 5832, 'label': '6O-1', 'order': 6, 'powers': [9, 4], 'representative': 3817, 'size': 162}
  • id: 164582652
    {'aut_label': '9A', 'centralizer': '36.e1.a1', 'counter': 45, 'group_counter': 166, 'group_order': 5832, 'label': '9A', 'order': 9, 'powers': [45, 7], 'representative': 1392, 'size': 36}
  • id: 164582653
    {'aut_label': '9A', 'centralizer': '36.e1.a1', 'counter': 46, 'group_counter': 166, 'group_order': 5832, 'label': '9B', 'order': 9, 'powers': [46, 7], 'representative': 3192, 'size': 36}
  • id: 164582654
    {'aut_label': '9A', 'centralizer': '36.e1.a1', 'counter': 47, 'group_counter': 166, 'group_order': 5832, 'label': '9C', 'order': 9, 'powers': [47, 7], 'representative': 1824, 'size': 36}
  • id: 164582655
    {'aut_label': '9D1', 'centralizer': '36.e1.a1', 'counter': 48, 'group_counter': 166, 'group_order': 5832, 'label': '9D1', 'order': 9, 'powers': [49, 7], 'representative': 1396, 'size': 36}
  • id: 164582656
    {'aut_label': '9D-1', 'centralizer': '36.e1.a1', 'counter': 49, 'group_counter': 166, 'group_order': 5832, 'label': '9D-1', 'order': 9, 'powers': [48, 7], 'representative': 2858, 'size': 36}
  • id: 164582658
    {'aut_label': '9D1', 'centralizer': '36.e1.a1', 'counter': 50, 'group_counter': 166, 'group_order': 5832, 'label': '9E1', 'order': 9, 'powers': [51, 7], 'representative': 5284, 'size': 36}
  • id: 164582659
    {'aut_label': '9D-1', 'centralizer': '36.e1.a1', 'counter': 51, 'group_counter': 166, 'group_order': 5832, 'label': '9E-1', 'order': 9, 'powers': [50, 7], 'representative': 4802, 'size': 36}
  • id: 164582660
    {'aut_label': '9D1', 'centralizer': '36.e1.a1', 'counter': 52, 'group_counter': 166, 'group_order': 5832, 'label': '9F1', 'order': 9, 'powers': [53, 7], 'representative': 1828, 'size': 36}
  • id: 164582661
    {'aut_label': '9D-1', 'centralizer': '36.e1.a1', 'counter': 53, 'group_counter': 166, 'group_order': 5832, 'label': '9F-1', 'order': 9, 'powers': [52, 7], 'representative': 3074, 'size': 36}
  • id: 164582662
    {'aut_label': '9G', 'centralizer': '54.z1.a1', 'counter': 54, 'group_counter': 166, 'group_order': 5832, 'label': '9G', 'order': 9, 'powers': [54, 6], 'representative': 936, 'size': 54}
  • id: 164582663
    {'aut_label': '9H1', 'centralizer': '54.ba1.a1', 'counter': 55, 'group_counter': 166, 'group_order': 5832, 'label': '9H1', 'order': 9, 'powers': [56, 6], 'representative': 1804, 'size': 54}
  • id: 164582664
    {'aut_label': '9H-1', 'centralizer': '54.ba1.a1', 'counter': 56, 'group_counter': 166, 'group_order': 5832, 'label': '9H-1', 'order': 9, 'powers': [55, 6], 'representative': 1010, 'size': 54}
  • id: 164582665
    {'aut_label': '12A1', 'centralizer': '54.bd1.a1', 'counter': 57, 'group_counter': 166, 'group_order': 5832, 'label': '12A1', 'order': 12, 'powers': [22, 18], 'representative': 666, 'size': 54}
  • id: 164582666
    {'aut_label': '12A1', 'centralizer': '54.bd1.a1', 'counter': 58, 'group_counter': 166, 'group_order': 5832, 'label': '12A-1', 'order': 12, 'powers': [22, 19], 'representative': 702, 'size': 54}
  • id: 164582667
    {'aut_label': '12B1', 'centralizer': '54.bi1.a1', 'counter': 59, 'group_counter': 166, 'group_order': 5832, 'label': '12B1', 'order': 12, 'powers': [23, 20], 'representative': 3921, 'size': 54}
  • id: 164582669
    {'aut_label': '12B1', 'centralizer': '54.bi1.a1', 'counter': 60, 'group_counter': 166, 'group_order': 5832, 'label': '12B-1', 'order': 12, 'powers': [23, 21], 'representative': 2013, 'size': 54}
  • id: 164582670
    {'aut_label': '12C1', 'centralizer': '81.d1.a1', 'counter': 61, 'group_counter': 166, 'group_order': 5832, 'label': '12C1', 'order': 12, 'powers': [27, 20], 'representative': 4235, 'size': 81}
  • id: 164582671
    {'aut_label': '12C-1', 'centralizer': '81.d1.a1', 'counter': 62, 'group_counter': 166, 'group_order': 5832, 'label': '12C-1', 'order': 12, 'powers': [28, 21], 'representative': 2107, 'size': 81}
  • id: 164582672
    {'aut_label': '12C-1', 'centralizer': '81.d1.a1', 'counter': 63, 'group_counter': 166, 'group_order': 5832, 'label': '12C5', 'order': 12, 'powers': [28, 20], 'representative': 2143, 'size': 81}
  • id: 164582673
    {'aut_label': '12C1', 'centralizer': '81.d1.a1', 'counter': 64, 'group_counter': 166, 'group_order': 5832, 'label': '12C-5', 'order': 12, 'powers': [27, 21], 'representative': 4199, 'size': 81}
  • id: 164582674
    {'aut_label': '12D1', 'centralizer': '81.b1.a1', 'counter': 65, 'group_counter': 166, 'group_order': 5832, 'label': '12D1', 'order': 12, 'powers': [27, 18], 'representative': 380, 'size': 81}
  • id: 164582675
    {'aut_label': '12D-1', 'centralizer': '81.b1.a1', 'counter': 66, 'group_counter': 166, 'group_order': 5832, 'label': '12D-1', 'order': 12, 'powers': [28, 19], 'representative': 3946, 'size': 81}
  • id: 164582676
    {'aut_label': '12D-1', 'centralizer': '81.b1.a1', 'counter': 67, 'group_counter': 166, 'group_order': 5832, 'label': '12D5', 'order': 12, 'powers': [28, 18], 'representative': 3910, 'size': 81}
  • id: 164582677
    {'aut_label': '12D1', 'centralizer': '81.b1.a1', 'counter': 68, 'group_counter': 166, 'group_order': 5832, 'label': '12D-5', 'order': 12, 'powers': [27, 19], 'representative': 416, 'size': 81}
  • id: 164582678
    {'aut_label': '12E1', 'centralizer': '162.x1.a1', 'counter': 69, 'group_counter': 166, 'group_order': 5832, 'label': '12E1', 'order': 12, 'powers': [32, 19], 'representative': 4110, 'size': 162}
  • id: 164582680
    {'aut_label': '12E1', 'centralizer': '162.x1.a1', 'counter': 70, 'group_counter': 166, 'group_order': 5832, 'label': '12E-1', 'order': 12, 'powers': [32, 18], 'representative': 4386, 'size': 162}
  • id: 164582681
    {'aut_label': '12F1', 'centralizer': '162.z1.a1', 'counter': 71, 'group_counter': 166, 'group_order': 5832, 'label': '12F1', 'order': 12, 'powers': [33, 18], 'representative': 5372, 'size': 162}
  • id: 164582682
    {'aut_label': '12F-1', 'centralizer': '162.z1.a1', 'counter': 72, 'group_counter': 166, 'group_order': 5832, 'label': '12F-1', 'order': 12, 'powers': [34, 19], 'representative': 1906, 'size': 162}
  • id: 164582683
    {'aut_label': '12F-1', 'centralizer': '162.z1.a1', 'counter': 73, 'group_counter': 166, 'group_order': 5832, 'label': '12F5', 'order': 12, 'powers': [34, 18], 'representative': 1942, 'size': 162}
  • id: 164582684
    {'aut_label': '12F1', 'centralizer': '162.z1.a1', 'counter': 74, 'group_counter': 166, 'group_order': 5832, 'label': '12F-5', 'order': 12, 'powers': [33, 19], 'representative': 5336, 'size': 162}
  • id: 164582685
    {'aut_label': '18A', 'centralizer': '36.e1.a1', 'counter': 75, 'group_counter': 166, 'group_order': 5832, 'label': '18A', 'order': 18, 'powers': [45, 24], 'representative': 660, 'size': 36}
  • id: 164582686
    {'aut_label': '18A', 'centralizer': '36.e1.a1', 'counter': 76, 'group_counter': 166, 'group_order': 5832, 'label': '18B', 'order': 18, 'powers': [46, 24], 'representative': 1308, 'size': 36}
  • id: 164582687
    {'aut_label': '18A', 'centralizer': '36.e1.a1', 'counter': 77, 'group_counter': 166, 'group_order': 5832, 'label': '18C', 'order': 18, 'powers': [47, 24], 'representative': 876, 'size': 36}
  • id: 164582688
    {'aut_label': '18D1', 'centralizer': '36.e1.a1', 'counter': 78, 'group_counter': 166, 'group_order': 5832, 'label': '18D1', 'order': 18, 'powers': [48, 24], 'representative': 662, 'size': 36}
  • id: 164582689
    {'aut_label': '18D-1', 'centralizer': '36.e1.a1', 'counter': 79, 'group_counter': 166, 'group_order': 5832, 'label': '18D-1', 'order': 18, 'powers': [49, 24], 'representative': 664, 'size': 36}
  • id: 164582691
    {'aut_label': '18D1', 'centralizer': '36.e1.a1', 'counter': 80, 'group_counter': 166, 'group_order': 5832, 'label': '18E1', 'order': 18, 'powers': [50, 24], 'representative': 2606, 'size': 36}
  • id: 164582692
    {'aut_label': '18D-1', 'centralizer': '36.e1.a1', 'counter': 81, 'group_counter': 166, 'group_order': 5832, 'label': '18E-1', 'order': 18, 'powers': [51, 24], 'representative': 2608, 'size': 36}
  • id: 164582693
    {'aut_label': '18D1', 'centralizer': '36.e1.a1', 'counter': 82, 'group_counter': 166, 'group_order': 5832, 'label': '18F1', 'order': 18, 'powers': [52, 24], 'representative': 878, 'size': 36}
  • id: 164582694
    {'aut_label': '18D-1', 'centralizer': '36.e1.a1', 'counter': 83, 'group_counter': 166, 'group_order': 5832, 'label': '18F-1', 'order': 18, 'powers': [53, 24], 'representative': 880, 'size': 36}
  • id: 164582695
    {'aut_label': '18G', 'centralizer': '54.z1.a1', 'counter': 84, 'group_counter': 166, 'group_order': 5832, 'label': '18G', 'order': 18, 'powers': [54, 23], 'representative': 3636, 'size': 54}
  • id: 164582696
    {'aut_label': '18H1', 'centralizer': '54.ba1.a1', 'counter': 85, 'group_counter': 166, 'group_order': 5832, 'label': '18H1', 'order': 18, 'powers': [55, 23], 'representative': 2990, 'size': 54}
  • id: 164582697
    {'aut_label': '18H-1', 'centralizer': '54.ba1.a1', 'counter': 86, 'group_counter': 166, 'group_order': 5832, 'label': '18H-1', 'order': 18, 'powers': [56, 23], 'representative': 5728, 'size': 54}
  • id: 164582698
    {'aut_label': '36A1', 'centralizer': '162.bi1.a1', 'counter': 87, 'group_counter': 166, 'group_order': 5832, 'label': '36A1', 'order': 36, 'powers': [84, 59], 'representative': 1101, 'size': 162}
  • id: 164582699
    {'aut_label': '36A1', 'centralizer': '162.bi1.a1', 'counter': 88, 'group_counter': 166, 'group_order': 5832, 'label': '36A-1', 'order': 36, 'powers': [84, 60], 'representative': 3801, 'size': 162}
  • id: 164582700
    {'aut_label': '36B1', 'centralizer': '162.bj1.a1', 'counter': 89, 'group_counter': 166, 'group_order': 5832, 'label': '36B1', 'order': 36, 'powers': [85, 59], 'representative': 5395, 'size': 162}
  • id: 164582702
    {'aut_label': '36B-1', 'centralizer': '162.bj1.a1', 'counter': 90, 'group_counter': 166, 'group_order': 5832, 'label': '36B-1', 'order': 36, 'powers': [86, 60], 'representative': 2699, 'size': 162}
  • id: 164582703
    {'aut_label': '36B-1', 'centralizer': '162.bj1.a1', 'counter': 91, 'group_counter': 166, 'group_order': 5832, 'label': '36B5', 'order': 36, 'powers': [86, 59], 'representative': 4679, 'size': 162}
  • id: 164582704
    {'aut_label': '36B1', 'centralizer': '162.bj1.a1', 'counter': 92, 'group_counter': 166, 'group_order': 5832, 'label': '36B-5', 'order': 36, 'powers': [85, 60], 'representative': 3415, 'size': 162}
• 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: 16437975
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16437986
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16437997
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16438008
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16438019
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 16438025
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438026
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1g', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438027
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -2, 2, -2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, 2, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -2, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 16438028
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -2, 2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -2, -2, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 16437976
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -2, -2, -2, -2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -2, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 16437979
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437980
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 16437981
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, -2, 0, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437982
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, -2, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 16437977
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1k', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, 2, 2, 2, -4, -4, 2, 2, -2, -2, 2, 2, -2, -4, 2, 4, -2, 2, -2, 4, -2, -2, -2, -2, 4, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 2, -4, 2, 2, 2, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437978
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.1l', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, 2, 2, 2, -4, -4, 2, 2, 2, 2, -2, -2, 2, 4, -2, -4, 2, -2, -2, 4, -2, -2, -2, -2, 4, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 2, -4, 2, 2, 2, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437983
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2e', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, 1, 1, 0, 4, 0, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, -2, 1, -2, 4, -2, -2, 4, 4, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1, -2, 1, 1, 1, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437984
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2f', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, 4, 0, 4, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, 0, 0, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, -2, 1, 1, 1, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 16437985
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2g', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, -4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437987
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2h', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437988
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2i', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, 1, 1, 0, -4, 0, -4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, -2, 1, -2, 4, -2, -2, -4, -4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -1, 2, -1, 2, -1, -1, -2, 1, 1, 1, -2, 1, 1, 1, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437989
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2j', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, -4, 0, -4, 0, 4, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, 0, 0, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, -2, 1, 1, 1, -2, 1, -2, 1, 2, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 16437992
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437993
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.4b', 'multiplicity': 1, 'nt': [12, 39], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437996
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.6a', 'multiplicity': 1, 'nt': [9, 18], 'qdim': 6, 'qvalues': [6, 6, 2, 2, 6, 6, 6, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 16437998
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.6b', 'multiplicity': 1, 'nt': [18, 51], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 6, 6, 6, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 16437999
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.6c', 'multiplicity': 1, 'nt': [36, 247], 'qdim': 6, 'qvalues': [6, -6, -2, 2, 6, 6, 6, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 3, 3, -6, -6, 3, 3, 3, 0, 0, 0, 2, 2, -2, -2, -1, 1, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 2}
  • id: 16438000
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.6d', 'multiplicity': 1, 'nt': [36, 247], 'qdim': 6, 'qvalues': [6, -6, 2, -2, 6, 6, 6, -3, -3, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, 3, 3, -6, -6, 3, 3, 3, 0, 0, 0, -2, -2, 2, 2, 1, -1, -1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 2}
  • id: 16437990
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2k', 'multiplicity': 4, 'nt': [24, 65], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, 8, 8, -4, -4, -4, -4, -4, -4, 8, -4, 2, 2, 0, 0, 0, 0, -8, -8, -8, 4, 4, 4, 4, 4, 4, -8, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, 2, -4, 2, -4, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, -2, -2, 4, 4, -8, 4, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437991
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.2l', 'multiplicity': 4, 'nt': [24, 65], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, 8, 8, -4, -4, -4, -4, -4, -4, 8, 8, -4, -4, 0, 0, 0, 0, -8, -8, -8, 4, 4, 4, 4, 4, 4, -8, -8, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, 2, 2, 2, -4, 2, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, -2, -2, 4, -2, 4, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437994
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.4c', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 8, 8, -4, -4, -4, -4, -4, -4, 8, -4, 2, 2, 0, 0, 0, 0, 8, 8, 8, -4, -4, -4, -4, -4, -4, 8, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, -1, 2, -1, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16437995
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.4d', 'multiplicity': 2, 'nt': [24, 544], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 8, 8, 8, -4, -4, -4, -4, -4, -4, 8, -4, 2, 2, 0, 0, 0, 0, -8, -8, -8, 4, 4, 4, 4, 4, 4, -8, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, -1, -1, -1, 2, -1, 2, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 1, -2, 1, 1, 1, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438001
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.6e', 'multiplicity': 2, 'nt': [18, 118], 'qdim': 12, 'qvalues': [12, 12, 4, 4, 12, 12, 12, 3, 3, -6, -6, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, 3, 3, -6, -6, 3, 3, -6, 0, 0, 0, -2, -2, -2, -2, 1, -2, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438002
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.6f', 'multiplicity': 2, 'nt': [36, 493], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 12, 12, 12, 3, 3, -6, -6, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 12, 12, 12, 3, 3, -6, -6, 3, 3, -6, 0, 0, 0, 2, 2, 2, 2, -1, 2, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438003
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.6g', 'multiplicity': 2, 'nt': [36, 997], 'qdim': 12, 'qvalues': [12, -12, -4, 4, 12, 12, 12, 3, 3, -6, -6, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, -3, -3, 6, 6, -3, -3, 6, 0, 0, 0, -2, -2, 2, 2, 1, 2, -1, -2, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438004
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.6h', 'multiplicity': 2, 'nt': [36, 997], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 12, 12, 12, 3, 3, -6, -6, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, -12, -12, -12, -3, -3, 6, 6, -3, -3, 6, 0, 0, 0, 2, 2, -2, -2, -1, -2, 1, 2, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438005
    {'cdim': 12, 'counter': 37, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12a', 'multiplicity': 1, 'nt': [18, 416], 'qdim': 12, 'qvalues': [12, 12, 0, 0, -6, -6, 3, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 3, -3, 3, 3, 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, 3, 3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438006
    {'cdim': 12, 'counter': 38, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12b', 'multiplicity': 1, 'nt': [18, 416], 'qdim': 12, 'qvalues': [12, 12, 0, 0, -6, -6, 3, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, -3, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, 3, 3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438007
    {'cdim': 12, 'counter': 39, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12c', 'multiplicity': 1, 'nt': [18, 416], 'qdim': 12, 'qvalues': [12, 12, 0, 0, -6, -6, 3, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3, 3, -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, -3, 0, -3, -3, 0, 0, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438009
    {'cdim': 12, 'counter': 40, 'faithful': True, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12d', 'multiplicity': 1, 'nt': [36, 6354], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -6, -6, 3, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, -3, 0, 3, -3, 3, 3, 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, -3, -3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438010
    {'cdim': 12, 'counter': 41, 'faithful': True, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12e', 'multiplicity': 1, 'nt': [36, 6354], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -6, -6, 3, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, -3, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, -3, -3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438011
    {'cdim': 12, 'counter': 42, 'faithful': True, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12f', 'multiplicity': 1, 'nt': [36, 6354], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -6, -6, 3, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3, 3, -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, 3, 0, 3, 3, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438018
    {'cdim': 18, 'counter': 49, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.18a', 'multiplicity': 1, 'nt': [27, 264], 'qdim': 18, 'qvalues': [18, 18, 0, 0, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
  • id: 16438020
    {'cdim': 18, 'counter': 50, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.18b', 'multiplicity': 1, 'nt': [27, 265], 'qdim': 18, 'qvalues': [18, 18, 0, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
  • id: 16438021
    {'cdim': 18, 'counter': 51, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.18c', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, 0, 0, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -6, -9, 18, -9, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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], 'schur_index': 1}
  • id: 16438022
    {'cdim': 18, 'counter': 52, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.18d', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, 18, 0, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, -6, 0, 18, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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], 'schur_index': 1}
  • id: 16438012
    {'cdim': 12, 'counter': 43, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12g', 'multiplicity': 2, 'nt': [36, 4173], 'qdim': 24, 'qvalues': [24, 24, 0, 0, -12, -12, 6, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 6, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -6, 3, -3, 3, 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, -6, 0, 3, 3, 0, 0, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438013
    {'cdim': 12, 'counter': 44, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12h', 'multiplicity': 2, 'nt': [36, 4173], 'qdim': 24, 'qvalues': [24, 24, 0, 0, -12, -12, 6, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 6, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, 0, -3, 3, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, -3, -3, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438014
    {'cdim': 12, 'counter': 45, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12i', 'multiplicity': 2, 'nt': [36, 4173], 'qdim': 24, 'qvalues': [24, 24, 0, 0, -12, -12, 6, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -12, -12, 6, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, -3, -6, -3, 6, 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, 6, -3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438015
    {'cdim': 12, 'counter': 46, 'faithful': True, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12j', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, -12, -12, 6, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, -6, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -6, 3, -3, 3, 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, 6, 0, -3, -3, 0, 0, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438016
    {'cdim': 12, 'counter': 47, 'faithful': True, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12k', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, -12, -12, 6, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, -6, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -3, 0, -3, 3, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -3, 3, 3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438017
    {'cdim': 12, 'counter': 48, 'faithful': True, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.12l', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -24, 0, 0, -12, -12, 6, -6, -6, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 12, 12, -6, 6, 6, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, -3, -6, -3, 6, 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, -6, 3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 16438023
    {'cdim': 18, 'counter': 53, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.18e', 'multiplicity': 2, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -36, 0, 0, -18, 36, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, -36, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 16438024
    {'cdim': 18, 'counter': 54, 'faithful': False, 'group': '5832.gj', 'group_order': 5832, 'image': None, 'label': '5832.gj.18f', 'multiplicity': 2, 'nt': [108, 0], 'qdim': 36, 'qvalues': [36, -36, 0, 0, 36, -18, -18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -36, 18, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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}
• 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: 36605614
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 5832, 'label': '5832.gj.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36605625
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 2916, 'label': '5832.gj.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36605636
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 2916, 'label': '5832.gj.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36605647
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 2916, 'label': '5832.gj.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36605658
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 1944, 'label': '5832.gj.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]]]}
  • id: 36605669
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 1944, 'label': '5832.gj.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]]]}
  • id: 36605680
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 1458, 'label': '5832.gj.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 36605691
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 1458, 'label': '5832.gj.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 36605702
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 1458, 'label': '5832.gj.1g1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 36605615
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 1458, 'label': '5832.gj.1g2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 36605616
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 972, 'label': '5832.gj.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]]]}
  • id: 36605617
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1.a1', 'kernel_order': 972, 'label': '5832.gj.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]]]}
  • id: 36605618
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 972, 'label': '5832.gj.1i1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]]]}
  • id: 36605619
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 972, 'label': '5832.gj.1i2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]]]}
  • id: 36605620
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 972, 'label': '5832.gj.1j1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]]]}
  • id: 36605621
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1.a1', 'kernel_order': 972, 'label': '5832.gj.1j2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]]]}
  • id: 36605622
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 17, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.b1', 'kernel_order': 486, 'label': '5832.gj.1k1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 0]], [[1, 4]], [[1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 3]], [[-1, 5]], [[1, 3]], [[1, 5]], [[-1, 1]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 3]], [[1, 5]], [[-1, 5]], [[-1, 3]], [[1, 1]], [[-1, 1]]]}
  • id: 36605623
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 18, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.b1', 'kernel_order': 486, 'label': '5832.gj.1k2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[1, 2]], [[1, 0]], [[-1, 2]], [[-1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[-1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 5]], [[1, 5]]]}
  • id: 36605624
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 19, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.b1', 'kernel_order': 486, 'label': '5832.gj.1k3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 4]], [[1, 0]], [[1, 4]], [[1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 3]], [[1, 5]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[1, 3]], [[-1, 1]], [[1, 1]]]}
  • id: 36605626
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 20, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.b1', 'kernel_order': 486, 'label': '5832.gj.1k4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 0]], [[1, 2]], [[1, 0]], [[-1, 2]], [[-1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 5]], [[-1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 5]], [[-1, 5]]]}
  • id: 36605627
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 21, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.a1', 'kernel_order': 486, 'label': '5832.gj.1l1', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 4]], [[-1, 0]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 3]], [[1, 5]], [[-1, 3]], [[-1, 5]], [[1, 1]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[1, 3]], [[1, 5]], [[-1, 5]], [[-1, 3]], [[1, 1]], [[-1, 1]]]}
  • id: 36605628
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 22, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.a1', 'kernel_order': 486, 'label': '5832.gj.1l2', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 5]], [[-1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[1, 3]], [[-1, 5]], [[1, 5]]]}
  • id: 36605629
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 23, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.a1', 'kernel_order': 486, 'label': '5832.gj.1l3', 'nt': [12, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 4]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 4]], [[-1, 0]], [[-1, 4]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 2]], [[1, 0]], [[1, 4]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 3]], [[-1, 5]], [[1, 3]], [[1, 5]], [[-1, 1]], [[-1, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 3]], [[-1, 5]], [[1, 5]], [[1, 3]], [[-1, 1]], [[1, 1]]]}
  • id: 36605630
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5832, 'counter': 24, 'cyclotomic_n': 12, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.2', 'image_order': 12, 'indicator': 0, 'kernel': '12.d1.a1', 'kernel_order': 486, 'label': '5832.gj.1l4', 'nt': [12, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 0]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[1, 4]], [[1, 0]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 5]], [[-1, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[-1, 4]], [[-1, 0]], [[1, 2]], [[1, 3]], [[1, 1]], [[-1, 1]], [[-1, 3]], [[1, 5]], [[-1, 5]]]}
  • id: 36605631
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 972, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.c1.a1', 'kernel_order': 972, 'label': '5832.gj.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36605632
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 972, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 972, 'label': '5832.gj.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 36605633
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 972, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 486, 'label': '5832.gj.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36605634
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 972, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 486, 'label': '5832.gj.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 36605635
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 972, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 324, 'label': '5832.gj.2e1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36605637
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 972, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 324, 'label': '5832.gj.2e2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[2, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36605638
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 972, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 324, 'label': '5832.gj.2f1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]]]}
  • id: 36605639
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 972, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 324, 'label': '5832.gj.2f2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]]]}
  • id: 36605640
    {'center': '6.c1.a1', 'center_index': 6, 'center_order': 972, 'counter': 33, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 243, 'label': '5832.gj.2g1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 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]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 36605641
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  • id: 36605642
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  • id: 36605643
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  • id: 36605644
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  • id: 36605645
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  • id: 36605646
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  • id: 36605648
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  • id: 36605649
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  • id: 36605650
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  • id: 36605651
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  • id: 36605652
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  • id: 36605653
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  • id: 36605654
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  • id: 36605655
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  • id: 36605656
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  • id: 36605657
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  • id: 36605659
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  • id: 36605660
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  • id: 36605661
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  • id: 36605662
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  • id: 36605663
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  • id: 36605664
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  • id: 36605665
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  • id: 36605666
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  • id: 36605667
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  • id: 36605668
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  • id: 36605670
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  • id: 36605671
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  • id: 36605672
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  • id: 36605673
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  • id: 36605674
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  • id: 36605675
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  • id: 36605676
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  • id: 36605677
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  • id: 36605678
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  • id: 36605679
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  • id: 36605681
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  • id: 36605682
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  • id: 36605683
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  • id: 36605684
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  • id: 36605685
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  • id: 36605686
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  • id: 36605687
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  • id: 36605688
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  • id: 36605689
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  • id: 36605690
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  • id: 36605692
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  • id: 36605693
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  • id: 36605694
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  • id: 36605695
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  • id: 36605696
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  • id: 36605697
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  • id: 36605698
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  • id: 36605699
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  • id: 36605700
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  • id: 36605701
    {'center': '972.b1.a1', 'center_index': 972, 'center_order': 6, 'counter': 89, 'cyclotomic_n': 4, 'dim': 18, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '1944.1307', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.b1.a1', 'kernel_order': 3, 'label': '5832.gj.18e1', 'nt': [108, 0], 'q_character': None, 'values': [[[18, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[0, 0]], [[6, 1]], [[9, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 36605703
    {'center': '972.b1.a1', 'center_index': 972, 'center_order': 6, 'counter': 90, 'cyclotomic_n': 4, 'dim': 18, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '1944.1307', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.b1.a1', 'kernel_order': 3, 'label': '5832.gj.18e2', 'nt': [108, 2], 'q_character': None, 'values': [[[18, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[-9, 0]], [[18, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[0, 0]], [[-6, 1]], [[9, 0]], [[-18, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 36605704
    {'center': '972.a1.a1', 'center_index': 972, 'center_order': 6, 'counter': 91, 'cyclotomic_n': 4, 'dim': 18, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '1944.1314', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1.a1', 'kernel_order': 3, 'label': '5832.gj.18f1', 'nt': [108, 0], 'q_character': None, 'values': [[[18, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 1]], [[0, 0]], [[6, 1]], [[0, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 36605705
    {'center': '972.a1.a1', 'center_index': 972, 'center_order': 6, 'counter': 92, 'cyclotomic_n': 4, 'dim': 18, 'faithful': False, 'field': [1, 0, 1], 'group': '5832.gj', 'group_counter': 166, 'group_order': 5832, 'image': None, 'image_isoclass': '1944.1314', 'image_order': 1944, 'indicator': 0, 'kernel': '1944.a1.a1', 'kernel_order': 3, 'label': '5832.gj.18f2', 'nt': [108, 2], 'q_character': None, 'values': [[[18, 0]], [[-18, 0]], [[0, 0]], [[0, 0]], [[18, 0]], [[-9, 0]], [[-9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 1]], [[0, 0]], [[-6, 1]], [[0, 0]], [[-18, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 227956576
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 5832, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '5832.gj.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5832.gj', 'subgroup_hash': 5408304993545916615, 'subgroup_order': 5832, 'subgroup_tex': '(C_3^3\\times C_6).S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 2916, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5799837917392304414, 'subgroup_order': 2916, 'subgroup_tex': 'C_2\\times (C_3^3.C_3^3):C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227956798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 2916, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.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': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2916.gv', 'subgroup_hash': 7443856842157632476, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4.C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956909
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 2916, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2916.gt', 'subgroup_hash': 1211319311655577790, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^4.C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227957020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1944, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.124', 'subgroup_hash': 124, 'subgroup_order': 1944, 'subgroup_tex': '(C_3^2\\times C_6).S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 972, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.1193', 'subgroup_hash': 1193, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 227957096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 972, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.3.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.1203', 'subgroup_hash': 1203, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3.(S_3\\times C_{12})', 'supersolvable': True, 'sylow': 0}
  • id: 227957107
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 1458, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': True, 'special_labels': ['F', 'C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1458.168', 'subgroup_hash': 168, 'subgroup_order': 1458, 'subgroup_tex': 'C_2\\times C_3^3.C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227957118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1458, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1458.839', 'subgroup_hash': 839, 'subgroup_order': 1458, 'subgroup_tex': 'C_9:C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1458, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1458.839', 'subgroup_hash': 839, 'subgroup_order': 1458, 'subgroup_tex': 'C_9:C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 972, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.228', 'subgroup_hash': 228, 'subgroup_order': 972, 'subgroup_tex': '(C_6\\times \\He_3).S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 972, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.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': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.329', 'subgroup_hash': 329, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3):C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956610
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 972, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.331', 'subgroup_hash': 331, 'subgroup_order': 972, 'subgroup_tex': '(C_3^3\\times C_6).S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 972, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.9', 'subgroup_hash': 9, 'subgroup_order': 972, 'subgroup_tex': '(C_6\\times \\He_3).S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956632
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 972, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.10', 'subgroup_hash': 10, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3).C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 486, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.604', 'subgroup_hash': 604, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.847', 'subgroup_hash': 847, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 486, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.606', 'subgroup_hash': 606, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956676
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 486, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.286', 'subgroup_hash': 286, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 486, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.288', 'subgroup_hash': 288, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4.C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956699
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 324, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.10', 'subgroup_hash': 10, 'subgroup_order': 972, 'subgroup_tex': '(C_3\\times \\He_3).C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 324, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.9', 'subgroup_hash': 9, 'subgroup_order': 972, 'subgroup_tex': '(C_6\\times \\He_3).S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 729, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '5832.gj.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '729.168', 'subgroup_hash': 168, 'subgroup_order': 729, 'subgroup_tex': 'C_3^3.C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 227956732
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.658', 'subgroup_hash': 658, 'subgroup_order': 648, 'subgroup_tex': 'C_3\\times C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '648.370', 'subgroup_hash': 370, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:(S_3\\times C_{12})', 'supersolvable': True, 'sylow': 0}
  • id: 227956754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '648.381', 'subgroup_hash': 381, 'subgroup_order': 648, 'subgroup_tex': 'C_9:(S_3\\times C_{12})', 'supersolvable': True, 'sylow': 0}
  • id: 227956765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.9.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '648.402', 'subgroup_hash': 402, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': True, 'sylow': 0}
  • id: 227956776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 324, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.9.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '648.53', 'subgroup_hash': 53, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:(C_4\\times D_9)', 'supersolvable': True, 'sylow': 0}
  • id: 227956787
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 486, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.196', 'subgroup_hash': 196, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 486, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.197', 'subgroup_hash': 197, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 486, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.64', 'subgroup_hash': 64, 'subgroup_order': 486, 'subgroup_tex': 'C_2\\times C_3^3.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 486, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.44', 'subgroup_hash': 44, 'subgroup_order': 486, 'subgroup_tex': '(C_3\\times \\He_3).S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 486, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.44', 'subgroup_hash': 44, 'subgroup_order': 486, 'subgroup_tex': '(C_3\\times \\He_3).S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 162, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.252', 'subgroup_hash': 252, 'subgroup_order': 486, 'subgroup_tex': 'C_{18}:C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.64', 'subgroup_hash': 64, 'subgroup_order': 486, 'subgroup_tex': 'C_2\\times C_3^3.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.64', 'subgroup_hash': 64, 'subgroup_order': 486, 'subgroup_tex': 'C_2\\times C_3^3.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956876
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.64', 'subgroup_hash': 64, 'subgroup_order': 486, 'subgroup_tex': 'C_2\\times C_3^3.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 243, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.103', 'subgroup_hash': 103, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 243, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.103', 'subgroup_hash': 103, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956910
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.232', 'subgroup_hash': 232, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.232', 'subgroup_hash': 232, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 243, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.105', 'subgroup_hash': 105, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 243, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.12.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.105', 'subgroup_hash': 105, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956954
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 324, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.104', 'subgroup_hash': 104, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': True, 'sylow': 0}
  • id: 227956965
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 324, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.20', 'subgroup_hash': 20, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times C_{18}).S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.173', 'subgroup_hash': 173, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956987
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.140', 'subgroup_hash': 140, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.140', 'subgroup_hash': 140, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.140', 'subgroup_hash': 140, 'subgroup_order': 324, 'subgroup_tex': 'C_9:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.144', 'subgroup_hash': 144, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.142', 'subgroup_hash': 142, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227957043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.f2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f2.a1', 'outer_equivalence': False, 'perfect': False, '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': '324.146', 'subgroup_hash': 146, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.63', 'subgroup_hash': 63, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227957065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.144', 'subgroup_hash': 144, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.146', 'subgroup_hash': 146, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.146', 'subgroup_hash': 146, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.144', 'subgroup_hash': 144, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.146', 'subgroup_hash': 146, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.63', 'subgroup_hash': 63, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227957086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.156', 'subgroup_hash': 156, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227957087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.156', 'subgroup_hash': 156, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227957088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': '324.93', 'subgroup_hash': 93, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227957089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.92', 'subgroup_hash': 92, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227957090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.a1', 'outer_equivalence': False, 'perfect': False, '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': '324.94', 'subgroup_hash': 94, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\times C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227957091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.a1', 'outer_equivalence': False, 'perfect': False, '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': '324.95', 'subgroup_hash': 95, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227957092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1.a1', 'outer_equivalence': False, 'perfect': False, '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': '324.92', 'subgroup_hash': 92, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227957093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1.a1', 'outer_equivalence': False, 'perfect': False, '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': '324.92', 'subgroup_hash': 92, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227957094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1.a1', 'outer_equivalence': False, 'perfect': False, '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': '324.7', 'subgroup_hash': 7, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 227957095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.18.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '324.7', 'subgroup_hash': 7, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 227957097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 243, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 243, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.38', 'subgroup_hash': 38, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4.C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 243, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.4', 'subgroup_hash': 4, 'subgroup_order': 243, 'subgroup_tex': 'C_3^3.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 81, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.63', 'subgroup_hash': 63, 'subgroup_order': 243, 'subgroup_tex': 'C_9:C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227957101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.4', 'subgroup_hash': 4, 'subgroup_order': 243, 'subgroup_tex': 'C_3^3.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.4', 'subgroup_hash': 4, 'subgroup_order': 243, 'subgroup_tex': 'C_3^3.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.4', 'subgroup_hash': 4, 'subgroup_order': 243, 'subgroup_tex': 'C_3^3.C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.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': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.27.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '216.120', 'subgroup_hash': 120, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.27.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '216.131', 'subgroup_hash': 131, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.27.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '216.50', 'subgroup_hash': 50, 'subgroup_order': 216, 'subgroup_tex': 'C_4\\times C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.27.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '216.53', 'subgroup_hash': 53, 'subgroup_order': 216, 'subgroup_tex': 'C_{36}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.27.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '216.34', 'subgroup_hash': 34, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.27.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '216.126', 'subgroup_hash': 126, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.27.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '216.28', 'subgroup_hash': 28, 'subgroup_order': 216, 'subgroup_tex': 'C_6.D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227957114
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 162, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.55', 'subgroup_hash': 55, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 162, 'counter': 87, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.48', 'subgroup_hash': 48, 'subgroup_order': 162, 'subgroup_tex': 'C_6\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 162, 'counter': 88, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.24', 'subgroup_hash': 24, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227957117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.48', 'subgroup_hash': 48, 'subgroup_order': 162, 'subgroup_tex': 'C_6\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957119
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.47', 'subgroup_hash': 47, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227957120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.e2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e2.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.24', 'subgroup_hash': 24, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227957122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.48', 'subgroup_hash': 48, 'subgroup_order': 162, 'subgroup_tex': 'C_6\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.48', 'subgroup_hash': 48, 'subgroup_order': 162, 'subgroup_tex': 'C_6\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.24', 'subgroup_hash': 24, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956578
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956580
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956583
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227956585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.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': 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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227956586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956587
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956590
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.q1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956591
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.q1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.e1', 'outer_equivalence': False, 'perfect': False, '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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.q1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.f1', 'outer_equivalence': False, 'perfect': False, '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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1.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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956595
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.38', 'subgroup_hash': 38, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956596
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.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': '162.38', 'subgroup_hash': 38, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.s2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s2.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.s2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s2.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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.5', 'subgroup_hash': 5, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956601
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.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': '162.5', 'subgroup_hash': 5, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956602
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956603
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956604
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956605
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956606
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956607
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.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': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.y1.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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956613
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '162.5', 'subgroup_hash': 5, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.36.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1.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': '162.5', 'subgroup_hash': 5, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956619
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956625
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.23', 'subgroup_hash': 23, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.23', 'subgroup_hash': 23, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956627
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.23', 'subgroup_hash': 23, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956628
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956629
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956635
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956636
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956639
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956640
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956641
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956642
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.r1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.s1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956645
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.t1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.u1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.v1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.y1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.6', 'subgroup_hash': 6, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 227956652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.7', 'subgroup_hash': 7, 'subgroup_order': 108, 'subgroup_tex': 'C_3:C_{36}', 'supersolvable': True, 'sylow': 0}
  • id: 227956653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956655
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.13', 'subgroup_hash': 13, 'subgroup_order': 108, 'subgroup_tex': 'C_4\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.be2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.be2.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956659
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956660
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bh2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bh2.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.9', 'subgroup_hash': 9, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.14', 'subgroup_hash': 14, 'subgroup_order': 108, 'subgroup_tex': 'C_9:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.11', 'subgroup_hash': 11, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 227956667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.54.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 81, 'counter': 182, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.21', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 21, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 227956669
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 81, 'counter': 183, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.27', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956670
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 81, 'counter': 184, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.27', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 27, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956671
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '81.11', 'subgroup_hash': 11, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.e2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e2.a1', 'outer_equivalence': False, 'perfect': False, '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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956677
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956679
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956680
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956683
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956684
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956690
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.72.o1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.o1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 227956692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.81.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': 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: 227956693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.81.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956694
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.81.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': 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: 227956695
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.81.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956696
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.81.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.81.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.81.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.21', 'subgroup_hash': 21, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956700
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.81.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 81, 'quotient_simple': 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: 227956701
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 54, 'counter': 211, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956702
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 54, 'counter': 212, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.38', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956703
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 18, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956704
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956705
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956706
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956707
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956708
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956709
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956711
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956713
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.k2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k2.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956714
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.m2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.m2.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956719
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956720
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956722
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q1.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956723
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956724
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.q2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q2.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956725
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.q2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q2.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956726
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.q2.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q2.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.r1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.s1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.s1.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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956730
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956731
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.t1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956734
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u1.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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.u1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.u2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u2.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.u2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u2.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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.u2.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u2.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.v1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.w1.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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.w1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.w1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956745
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.x1.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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.x1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.y1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.y1.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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.y1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.y1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956751
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z1.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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956752
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ba1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ba1.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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956755
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bb1.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': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227956757
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956758
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc1.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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bd1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956760
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bd1.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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956761
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be1.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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bf1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bf1.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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bg1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bg1.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bh1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bh1.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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956771
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1.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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956772
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bi1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bi1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bi1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1.e1', 'outer_equivalence': False, 'perfect': False, '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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bi1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1.f1', 'outer_equivalence': False, 'perfect': False, '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': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956777
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bj1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bj1.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': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bk1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956780
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bk1.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bk1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bk1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bk1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bk1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bk1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bk1.e1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bk1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bk1.f1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bl1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956786
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bl1.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956788
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bl1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bl1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956790
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bl1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bl1.e1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bl1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bl1.f1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bm1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bm1.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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bm1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bm1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bm1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bm1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bm1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bm1.e1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bm1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bm1.f1', 'outer_equivalence': False, 'perfect': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956800
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bn1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bn1.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': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956802
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bo1.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': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956805
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.108.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bp1.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': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956806
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956807
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956808
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956809
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956812
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956813
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956814
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956815
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956816
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956817
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956818
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956819
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956822
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': 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: 227956823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956824
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': 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: 227956825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.q1.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': 162, 'quotient_simple': 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: 227956826
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': 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: 227956827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956829
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956833
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 227956834
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 227956836
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956837
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956838
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956839
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 227956840
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956841
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956842
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956845
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956846
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 342, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956847
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 343, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956849
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956851
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.162.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 227956852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 27, 'counter': 348, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.36', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956853
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 27, 'counter': 349, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.120', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 120, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 9, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956857
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956860
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956861
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956862
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956863
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956864
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.k2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k2.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956866
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956867
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956868
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.m2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m2.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956869
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956870
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956871
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956873
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1.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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.q2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q2.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956877
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.q2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q2.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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.q2.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q2.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956879
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.r1.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.s1.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956881
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.s1.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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956883
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.t1.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 227956884
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u1.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956885
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u1.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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.u1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.u2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u2.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.u2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u2.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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.u2.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u2.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.v1.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956892
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.w1.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.w1.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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.w1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.w1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.x1.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.x1.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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.x1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.x1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.y1.a1', 'outer_equivalence': False, 'perfect': False, '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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.y1.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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.216.y1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.y1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956902
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.243.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.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': 243, 'quotient_simple': None, '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: 227956903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.243.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.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': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 227956904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.243.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.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': 243, 'quotient_simple': None, '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: 227956905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.243.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.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': 243, 'quotient_simple': None, '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: 227956906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.243.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '243.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': 243, 'quotient_simple': None, '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: 227956907
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': True, 'core_order': 18, 'counter': 398, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '324.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '324.117', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 117, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:D_6', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, '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: 227956908
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 6, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956911
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956912
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956913
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956914
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956915
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 6, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956916
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956917
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956918
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956919
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956920
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 409, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.324.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956922
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 410, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.324.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956923
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 2, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 2, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956926
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 2, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956927
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956929
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 2, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956930
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 418, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.324.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956931
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 419, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.324.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.u1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956933
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 420, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.324.u1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.u1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956934
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 421, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.324.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956935
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 422, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.324.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.v1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956936
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 423, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.324.v1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.v1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 227956937
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956938
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956939
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956940
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.y2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.y2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956942
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.z1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227956944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956945
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.ba1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956947
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bb1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956948
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956949
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bc1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956950
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bd1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956952
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.be1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bf1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bg1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956959
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bh1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956961
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bi1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956964
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bj1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bk1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956969
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bl1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956971
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bm1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956972
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956973
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 3, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bn1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bo1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227956977
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956978
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bp1.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': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956979
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bp1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bp1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956980
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bp1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bp1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956981
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bp1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bp1.e1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956982
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.324.bp1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.bp1.f1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 227956983
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956984
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956985
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956989
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956991
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 473, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.486.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956992
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956993
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956994
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 476, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.486.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956995
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 477, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.486.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956996
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 478, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.486.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956997
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227956999
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227957000
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 481, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.486.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, 'quotient_simple': 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: 227957001
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.486.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '486.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': 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: 227957002
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 483, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.486.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': 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: 227957003
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': True, 'core_order': 9, 'counter': 484, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5832.gj.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.375', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 375, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6.S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['C7'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957004
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957005
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957006
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957007
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957008
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957010
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957011
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957012
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957014
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957015
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 495, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.648.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227957016
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 496, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.648.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227957017
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957018
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957022
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957023
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957024
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957025
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957026
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 504, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.648.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227957027
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 505, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.648.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.u1.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227957028
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 506, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.648.u1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.u1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227957029
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 507, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.648.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227957030
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 508, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.648.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.v1.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': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227957031
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 509, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.648.v1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.v1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 227957033
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957034
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957035
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957036
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.648.y2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.y2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 227957037
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '5832.gj.729.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '729.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': 729, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 2}
  • id: 227957038
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2916, 'characteristic': True, 'core_order': 6, 'counter': 515, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5832.gj.972.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '972.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '972.446', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 446, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 972, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957039
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2916, 'characteristic': True, 'core_order': 6, 'counter': 516, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5832.gj.972.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '972.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '972.445', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 445, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 972, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957040
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': False, 'core_order': 2, 'counter': 517, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957041
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 2, 'counter': 518, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957042
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 2, 'counter': 519, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957044
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 2, 'counter': 520, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957045
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 521, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957046
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 522, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957047
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 523, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957048
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 524, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957049
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 525, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957050
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 526, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957051
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 527, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957052
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 528, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957053
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 529, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.972.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 227957055
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.972.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957056
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.972.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957057
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.972.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957058
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.972.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957059
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.972.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957060
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.972.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957061
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.972.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957062
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.972.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '972.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': 972, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957063
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5832.gj.1458.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.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': 1458, 'quotient_simple': 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: 227957064
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 539, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.1458.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.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': 1458, 'quotient_simple': 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: 227957066
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 540, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.1458.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1458.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': 1458, 'quotient_simple': 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: 227957067
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2916, 'characteristic': True, 'core_order': 3, 'counter': 541, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5832.gj.1944.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1944.1314', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1314, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3.(S_3\\times C_{12})', 'simple': True, 'solvable': True, 'special_labels': ['C8'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957068
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2916, 'characteristic': True, 'core_order': 3, 'counter': 542, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5832.gj.1944.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1944.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1944.1307', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1307, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:(S_3\\times C_{12})', 'simple': True, 'solvable': True, 'special_labels': ['C8'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 227957069
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1458, 'characteristic': False, 'core_order': 1, 'counter': 543, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.1944.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.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': 1944, '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: 227957070
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 544, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.1944.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.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': 1944, '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: 227957071
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 545, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.1944.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.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': 1944, '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: 227957072
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 1, 'counter': 546, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.1944.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.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': 1944, '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: 227957073
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 547, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.1944.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.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': 1944, '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: 227957074
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 548, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.1944.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.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': 1944, '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: 227957075
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 549, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.1944.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1944.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': 1944, '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: 227957077
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 5832, 'characteristic': True, 'core_order': 2, 'counter': 550, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5832.gj.2916.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '2916.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2916.ef', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7107432785865780292, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 2916, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^4.S_3^2', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 227957078
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 551, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.2916.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.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': 2916, '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: 227957079
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 552, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '5832.gj.2916.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2916.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': 2916, '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: 227957080
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.gj', 'ambient_counter': 166, 'ambient_order': 5832, 'ambient_tex': '(C_3^3\\times C_6).S_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 5832, 'characteristic': True, 'core_order': 1, 'counter': 553, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '5832.gj.5832.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '5832.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '5832.gj', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5408304993545916615, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 5832, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_3^3\\times C_6).S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C9'], '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: 227956607
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.b1', '18.j1.a1'], 'contains': ['72.i1.a1', '108.bd1.b1', '108.bg1.b1', '108.bp1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3863, -1, 5800, -1, 3727, -1, 5872, -1], 'generators': [3, 1944, 578, 3096, 4104], 'label': '5832.gj.36.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.w1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.b1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956576
    {'ambient': '5832.gj', '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': '2916.a1.a1', 'complements': ['5832.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '3.b1.a1', '3.c1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7494, 3843, 7565, 5948, 6316, 4460, 7740, 5949], 'generators': [3, 1944, 24, 3096, 18, 36, 216, 288, 2], 'label': '5832.gj.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.c1.a1', '2.b1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '2916.ef', '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': '2916.ef'}
  • id: 227956577
    {'ambient': '5832.gj', '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': '2916.a1.a1', 'complements': ['1458.b1.a1', '1458.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.d1.b1', '12.i1.b1', '12.j1.b1', '12.k1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3582, 701, 4960, 626, 3338, 617, 5591, 1773], 'generators': [3, 216, 288, 2, 1944, 24, 3096], 'label': '5832.gj.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '5832.gj', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2916.ef'}
  • id: 227956578
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1'], 'contains': ['72.n1.a1', '108.p1.a1', '108.q1.a1', '108.q1.b1', '108.q2.b1', '108.u1.a1', '108.u1.b1', '108.u2.b1', '108.w1.a1', '108.w1.b1', '108.x1.a1', '108.y1.a1', '108.y1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1728, -1, 4325, -1, 1094, -1, 3377, -1], 'generators': [36, 2160, 2, 1464, 2448], 'label': '5832.gj.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '36.n1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956579
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1'], 'contains': ['72.n1.b1', '108.p1.a1', '108.q1.a1', '108.q1.c1', '108.q2.a1', '108.u1.a1', '108.u1.c1', '108.u2.a1', '108.w1.a1', '108.w1.c1', '108.x1.b1', '108.y1.a1', '108.y1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1728, -1, 4567, -1, 1094, -1, 3089, -1], 'generators': [36, 2160, 2, 3408, 2448], 'label': '5832.gj.36.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '36.n1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956580
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1'], 'contains': ['72.n1.c1', '108.p1.a1', '108.q1.b1', '108.q1.c1', '108.q2.c1', '108.u1.b1', '108.u1.c1', '108.u2.c1', '108.w1.b1', '108.w1.c1', '108.x1.c1', '108.y1.b1', '108.y1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1728, -1, 4700, -1, 1094, -1, 3305, -1], 'generators': [36, 2160, 2, 5352, 2448], 'label': '5832.gj.36.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '36.n1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956581
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.d1.a1'], 'contains': ['72.o1.a1', '108.q1.b1', '108.q2.a1', '108.s1.a1', '108.s1.b1', '108.t1.a1', '108.u1.b1', '108.u2.a1', '108.x1.a1', '108.y1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1597, -1, 2221, -1, 989, -1, 2718, -1], 'generators': [36, 2160, 1946, 1464, 2448], 'label': '5832.gj.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.o1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956582
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.d1.b1'], 'contains': ['72.o1.b1', '108.q1.a1', '108.q2.c1', '108.s1.a1', '108.s1.c1', '108.t1.a1', '108.u1.a1', '108.u2.c1', '108.x1.b1', '108.y1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1597, -1, 4000, -1, 989, -1, 2863, -1], 'generators': [36, 2160, 1946, 3408, 2448], 'label': '5832.gj.36.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.o1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956583
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.d1.c1'], 'contains': ['72.o1.c1', '108.q1.c1', '108.q2.b1', '108.s1.b1', '108.s1.c1', '108.t1.a1', '108.u1.c1', '108.u2.b1', '108.x1.c1', '108.y1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1597, -1, 2855, -1, 989, -1, 3233, -1], 'generators': [36, 2160, 1946, 5352, 2448], 'label': '5832.gj.36.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.o1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956584
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.j1.a1', '12.k1.a1', '18.c1.a1'], 'contains': ['72.a1.a1', '108.z1.a1', '108.ba1.a1', '108.bb1.a1', '108.bc1.a1', '108.bd1.a1', '108.be1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3211, -1, 5732, -1, 3390, -1, 5094, -1], 'generators': [39, 1944, 2, 288, 4104], 'label': '5832.gj.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956585
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.j1.b1', '12.k1.b1', '18.c1.a1'], 'contains': ['72.a1.a1', '108.z1.b1', '108.ba1.b1', '108.bb1.b1', '108.bc1.b1', '108.bd1.b1', '108.be1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3211, -1, 5266, -1, 3390, -1, 4960, -1], 'generators': [3, 1944, 2, 288, 4104], 'label': '5832.gj.36.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.p1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956586
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.d1.a1'], 'contains': ['72.o1.a1', '108.bb1.a1', '108.bi1.a1', '108.bk1.a1', '108.bl1.a1', '108.bm1.a1'], 'core': '5832.a1.a1', 'coset_action_label': '36T6354', 'count': 18, 'diagramx': [562, -1, 804, -1, 266, -1, 1303, -1], 'generators': [39, 2160, 2, 2232, 3552], 'label': '5832.gj.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.q1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956587
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.d1.b1'], 'contains': ['72.o1.b1', '108.bb1.a1', '108.bi1.c1', '108.bk1.c1', '108.bl1.c1', '108.bm1.b1'], 'core': '5832.a1.a1', 'coset_action_label': '36T6354', 'count': 18, 'diagramx': [562, -1, 1709, -1, 266, -1, 1376, -1], 'generators': [39, 2160, 2, 2232, 5496], 'label': '5832.gj.36.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '36.q1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956588
    {'ambient': '5832.gj', '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': '2916.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.d1.a1', '12.d1.b1', '18.k1.a1', '18.l1.a1', '18.m1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6016, 1844, 5916, 3023, 4268, 2165, 6289, 3151], 'generators': [3, 216, 288, 36, 1944, 24, 3096], 'label': '5832.gj.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.c1.a1', '12.d1.a1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2916.ef'}
  • id: 227956589
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.d1.c1'], 'contains': ['72.o1.c1', '108.bb1.a1', '108.bi1.b1', '108.bk1.b1', '108.bl1.b1', '108.bm1.c1'], 'core': '5832.a1.a1', 'coset_action_label': '36T6354', 'count': 18, 'diagramx': [562, -1, 1361, -1, 266, -1, 2370, -1], 'generators': [39, 2160, 2, 2232, 1608], 'label': '5832.gj.36.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '36.q1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956590
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.d1.a1'], 'contains': ['72.o1.a1', '108.bb1.b1', '108.bi1.d1', '108.bk1.d1', '108.bl1.d1', '108.bm1.d1'], 'core': '5832.a1.a1', 'coset_action_label': '36T6354', 'count': 18, 'diagramx': [562, -1, 550, -1, 266, -1, 774, -1], 'generators': [3, 2160, 2, 2232, 3552], 'label': '5832.gj.36.q1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.q1.d1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956591
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.d1.b1'], 'contains': ['72.o1.b1', '108.bb1.b1', '108.bi1.f1', '108.bk1.f1', '108.bl1.f1', '108.bm1.e1'], 'core': '5832.a1.a1', 'coset_action_label': '36T6354', 'count': 18, 'diagramx': [562, -1, 1270, -1, 266, -1, 860, -1], 'generators': [3, 2160, 2, 2232, 5496], 'label': '5832.gj.36.q1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '36.q1.e1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.e1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956592
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.d1.c1'], 'contains': ['72.o1.c1', '108.bb1.b1', '108.bi1.e1', '108.bk1.e1', '108.bl1.e1', '108.bm1.f1'], 'core': '5832.a1.a1', 'coset_action_label': '36T6354', 'count': 18, 'diagramx': [562, -1, 670, -1, 266, -1, 1231, -1], 'generators': [3, 2160, 2, 2232, 1608], 'label': '5832.gj.36.q1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '36.q1.f1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.f1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956593
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.e1.a1'], 'contains': ['72.d1.a1', '108.bc1.a1', '108.bj1.a1', '108.bn1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4144, -1, 6190, -1, 4139, -1, 5341, -1], 'generators': [39, 1944, 2, 24, 4104], 'label': '5832.gj.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.r1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.a1', 'subgroup_fusion': None, 'weyl_group': '486.103'}
  • id: 227956594
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '18.e1.a1'], 'contains': ['72.d1.a1', '108.bc1.b1', '108.bj1.b1', '108.bn1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4144, -1, 5868, -1, 4139, -1, 5292, -1], 'generators': [3, 1944, 2, 24, 4104], 'label': '5832.gj.36.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.r1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.b1', 'subgroup_fusion': None, 'weyl_group': '486.103'}
  • id: 227956595
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.f1.a1'], 'contains': ['72.e1.a1', '108.bc1.a1', '108.bi1.a1', '108.bi1.b1', '108.bi1.c1', '108.bo1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [835, -1, 1580, -1, 1238, -1, 1523, -1], 'generators': [39, 2160, 2, 3768, 1944], 'label': '5832.gj.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.s1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956596
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.f1.a1'], 'contains': ['72.e1.a1', '108.bc1.b1', '108.bi1.d1', '108.bi1.e1', '108.bi1.f1', '108.bo1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [835, -1, 1018, -1, 1238, -1, 1007, -1], 'generators': [3, 2160, 2, 3768, 1944], 'label': '5832.gj.36.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.s1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.b1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956597
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.s2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.f2.a1'], 'contains': ['72.e2.a1', '108.bc1.a1', '108.bk1.a1', '108.bk1.b1', '108.bk1.c1', '108.bo1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [985, -1, 1645, -1, 1346, -1, 1597, -1], 'generators': [39, 2160, 290, 3768, 1944], 'label': '5832.gj.36.s2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.s2.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s2.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956598
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.s2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.f2.a1'], 'contains': ['72.e2.a1', '108.bc1.b1', '108.bk1.d1', '108.bk1.e1', '108.bk1.f1', '108.bo1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [985, -1, 1082, -1, 1346, -1, 1081, -1], 'generators': [3, 2160, 290, 3768, 1944], 'label': '5832.gj.36.s2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.s2.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s2.b1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956599
    {'ambient': '5832.gj', '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': '972.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.a1.a1', '18.o1.a1', '18.q1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8129, 9299, 8220, 9374, 6961, 9182, 8502, 9399], 'generators': [21, 4104, 4392, 2, 1944, 36, 24], 'label': '5832.gj.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.a1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '972.445'}
  • id: 227956600
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.g1.a1'], 'contains': ['72.f1.a1', '108.bc1.a1', '108.bp1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3680, -1, 5193, -1, 3144, -1, 5662, -1], 'generators': [39, 1944, 2, 3096, 4104], 'label': '5832.gj.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '36.t1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': '486.105'}
  • id: 227956601
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.b1', '18.g1.a1'], 'contains': ['72.f1.a1', '108.bc1.b1', '108.bp1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3680, -1, 5026, -1, 3144, -1, 5507, -1], 'generators': [3, 1944, 2, 3096, 4104], 'label': '5832.gj.36.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '36.t1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.b1', 'subgroup_fusion': None, 'weyl_group': '486.105'}
  • id: 227956602
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.h1.a1'], 'contains': ['72.g1.a1', '108.bd1.a1', '108.bf1.a1', '108.bn1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4922, -1, 7006, -1, 5073, -1, 6670, -1], 'generators': [39, 1944, 578, 24, 4104], 'label': '5832.gj.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.u1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956603
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '18.h1.a1'], 'contains': ['72.g1.a1', '108.bd1.b1', '108.bf1.b1', '108.bn1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4922, -1, 6965, -1, 5073, -1, 6549, -1], 'generators': [3, 1944, 578, 24, 4104], 'label': '5832.gj.36.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.u1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.b1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956604
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.i1.a1'], 'contains': ['72.h1.a1', '108.bd1.a1', '108.bl1.a1', '108.bl1.b1', '108.bl1.c1', '108.bo1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2159, -1, 1149, -1, 1456, -1, 1450, -1], 'generators': [39, 2160, 578, 3768, 1944], 'label': '5832.gj.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.v1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956605
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '18.i1.a1'], 'contains': ['72.h1.a1', '108.bd1.b1', '108.bl1.d1', '108.bl1.e1', '108.bl1.f1', '108.bo1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2159, -1, 926, -1, 1456, -1, 934, -1], 'generators': [3, 2160, 578, 3768, 1944], 'label': '5832.gj.36.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.v1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.b1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956606
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.j1.a1'], 'contains': ['72.i1.a1', '108.bd1.a1', '108.bg1.a1', '108.bp1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3863, -1, 6064, -1, 3727, -1, 5948, -1], 'generators': [39, 1944, 578, 3096, 4104], 'label': '5832.gj.36.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.w1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956608
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.i1.a1', '18.k1.a1'], 'contains': ['72.b1.a1', '108.be1.a1', '108.bh1.a1', '108.bn1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4376, -1, 5925, -1, 4209, -1, 6270, -1], 'generators': [39, 1944, 288, 24, 4104], 'label': '5832.gj.36.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.x1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956609
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.i1.b1', '18.k1.a1'], 'contains': ['72.b1.a1', '108.be1.b1', '108.bh1.b1', '108.bn1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4376, -1, 5662, -1, 4209, -1, 6059, -1], 'generators': [3, 1944, 288, 24, 4104], 'label': '5832.gj.36.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.x1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.b1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956610
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': ['972.p1.b1', '972.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.c1.a1'], 'contains': ['12.b1.a1', '18.b1.a1', '18.n1.a1', '18.r1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7524, 7629, 8164, 5111, 6652, 8012, 7603, 5922], 'generators': [18, 216, 4392, 2, 1944, 36, 3096], 'label': '5832.gj.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.b1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '972.446'}
  • id: 227956611
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.j1.a1', '18.l1.a1'], 'contains': ['72.k1.a1', '108.be1.a1', '108.bm1.a1', '108.bm1.b1', '108.bm1.c1', '108.bo1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2459, -1, 4181, -1, 1787, -1, 2080, -1], 'generators': [39, 2160, 288, 3768, 1944], 'label': '5832.gj.36.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.y1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956612
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.j1.b1', '18.l1.a1'], 'contains': ['72.k1.a1', '108.be1.b1', '108.bm1.d1', '108.bm1.e1', '108.bm1.f1', '108.bo1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2459, -1, 3501, -1, 1787, -1, 1157, -1], 'generators': [3, 2160, 288, 3768, 1944], 'label': '5832.gj.36.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.y1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.b1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956613
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.k1.a1', '18.m1.a1'], 'contains': ['72.c1.a1', '108.be1.a1', '108.bp1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3954, -1, 5338, -1, 3292, -1, 5560, -1], 'generators': [39, 1944, 288, 3096, 4104], 'label': '5832.gj.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.z1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956614
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.k1.b1', '18.m1.a1'], 'contains': ['72.c1.a1', '108.be1.b1', '108.bp1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3954, -1, 4898, -1, 3292, -1, 5392, -1], 'generators': [3, 1944, 288, 3096, 4104], 'label': '5832.gj.36.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.z1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.b1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956615
    {'ambient': '5832.gj', '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': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '27.a1.a1'], 'contains': ['108.j1.a1', '108.z1.a1', '108.z1.b1', '162.a1.a1', '162.b1.a1', '162.c1.a1', '162.d1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5217, -1, 7748, -1, 5760, -1, 6480, -1], 'generators': [3, 216, 36, 2, 4392], 'label': '5832.gj.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '2916.ef', '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': '12.4'}
  • id: 227956616
    {'ambient': '5832.gj', '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': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '27.b1.a1'], 'contains': ['108.l1.a1', '108.ba1.a1', '108.ba1.b1', '162.a1.a1', '162.e1.a1', '162.f1.a1', '162.g1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5044, -1, 7827, -1, 5385, -1, 6129, -1], 'generators': [3, 1944, 36, 2, 4392], 'label': '5832.gj.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.b1.a1', 'projective_image': '2916.ef', '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': '12.4'}
  • id: 227956617
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.d1.a1', '18.d1.b1', '18.d1.c1'], 'contains': ['108.t1.a1', '108.bb1.a1', '108.bb1.b1', '162.a1.a1', '162.h1.a1', '162.i1.a1', '162.j1.a1', '162.k1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2678, -1, 690, -1, 2638, -1, 4111, -1], 'generators': [3, 4104, 36, 2, 4392], 'label': '5832.gj.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '54.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956618
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.e1.a1', '18.f1.a1', '18.f2.a1', '18.g1.a1'], 'contains': ['108.c1.a1', '108.bc1.a1', '108.bc1.b1', '162.b1.a1', '162.e1.a1', '162.h1.a1', '162.i1.a1', '162.l1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3533, -1, 5446, -1, 3501, -1, 5170, -1], 'generators': [3, 1944, 36, 2, 216], 'label': '5832.gj.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '54.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 227956619
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.h1.a1', '18.i1.a1', '18.j1.a1', '27.c1.a1'], 'contains': ['108.a1.a1', '108.bd1.a1', '108.bd1.b1', '162.c1.a1', '162.f1.a1', '162.j1.a1', '162.l1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5604, -1, 6784, -1, 4864, -1, 6330, -1], 'generators': [3, 1944, 36, 578, 4104], 'label': '5832.gj.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956620
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.k1.a1', '18.l1.a1', '18.m1.a1', '27.d1.a1'], 'contains': ['108.b1.a1', '108.be1.a1', '108.be1.b1', '162.d1.a1', '162.g1.a1', '162.k1.a1', '162.l1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6136, -1, 6147, -1, 4556, -1, 6210, -1], 'generators': [3, 1944, 36, 288, 4104], 'label': '5832.gj.54.f1.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.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956621
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': ['972.j1.b1', '972.k1.b1', '972.j1.a1', '972.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '18.b1.a1', '18.t1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7729, 3933, 8033, 6720, 6549, 3705, 7532, 7069], 'generators': [18, 216, 288, 24, 1944, 36, 3096], 'label': '5832.gj.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '972.446'}
  • id: 227956622
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '27.e1.a1'], 'contains': ['108.k1.a1', '108.bf1.a1', '108.bf1.b1', '162.c1.a1', '162.m1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6780, -1, 9076, -1, 7052, -1, 7477, -1], 'generators': [3, 216, 36, 2306, 24], 'label': '5832.gj.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '54.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956623
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '27.f1.a1'], 'contains': ['108.m1.a1', '108.bg1.a1', '108.bg1.b1', '162.f1.a1', '162.o1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5705, -1, 7508, -1, 5266, -1, 6893, -1], 'generators': [3, 1944, 36, 2306, 1152], 'label': '5832.gj.54.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '54.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956624
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '27.g1.a1'], 'contains': ['108.n1.a1', '108.bh1.a1', '108.bh1.b1', '162.g1.a1', '162.n1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6622, -1, 7582, -1, 6015, -1, 7380, -1], 'generators': [3, 1944, 36, 4392, 24], 'label': '5832.gj.54.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.g1.a1', 'old_label': '54.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956625
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.f1.a1'], 'contains': ['108.q2.a1', '108.bi1.a1', '108.bi1.d1', '162.h1.a1', '162.q1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1050, -1, 173, -1, 575, -1, 1737, -1], 'generators': [3, 2160, 36, 2, 3552], 'label': '5832.gj.54.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '54.j1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956626
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.c1', '18.f1.a1'], 'contains': ['108.q2.b1', '108.bi1.b1', '108.bi1.e1', '162.h1.a1', '162.q1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1050, -1, 505, -1, 575, -1, 2508, -1], 'generators': [3, 2160, 36, 2, 1608], 'label': '5832.gj.54.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '54.j1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956627
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '18.f1.a1'], 'contains': ['108.q2.c1', '108.bi1.c1', '108.bi1.f1', '162.h1.a1', '162.q1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1050, -1, 1413, -1, 575, -1, 1940, -1], 'generators': [3, 2160, 36, 2, 5496], 'label': '5832.gj.54.j1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '54.j1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956628
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1'], 'contains': ['108.r1.a1', '108.bj1.a1', '108.bj1.b1', '162.i1.a1', '162.p1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4042, -1, 6588, -1, 4433, -1, 4682, -1], 'generators': [3, 4104, 36, 2, 24], 'label': '5832.gj.54.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1.a1', 'old_label': '54.k1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956629
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.f2.a1'], 'contains': ['108.s1.a1', '108.bk1.a1', '108.bk1.d1', '162.i1.a1', '162.q1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1142, -1, 562, -1, 674, -1, 1803, -1], 'generators': [3, 2160, 36, 2234, 3552], 'label': '5832.gj.54.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '54.l1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956630
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.c1', '18.f2.a1'], 'contains': ['108.s1.b1', '108.bk1.b1', '108.bk1.e1', '162.i1.a1', '162.q1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1142, -1, 789, -1, 674, -1, 2574, -1], 'generators': [3, 2160, 36, 2234, 1608], 'label': '5832.gj.54.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '54.l1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956631
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '18.f2.a1'], 'contains': ['108.s1.c1', '108.bk1.c1', '108.bk1.f1', '162.i1.a1', '162.q1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1142, -1, 1485, -1, 674, -1, 2006, -1], 'generators': [3, 2160, 36, 2234, 5496], 'label': '5832.gj.54.l1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '54.l1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956632
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': ['972.j1.b1', '972.k1.b1', '972.j1.a1', '972.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '18.a1.a1', '18.v1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6973, 6166, 6730, 8107, 6014, 6723, 7900, 8286], 'generators': [21, 216, 288, 1152, 1944, 36, 24], 'label': '5832.gj.6.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '972.445'}
  • id: 227956633
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.i1.a1'], 'contains': ['108.u2.a1', '108.bl1.a1', '108.bl1.d1', '162.j1.a1', '162.q1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1243, -1, 58, -1, 779, -1, 1671, -1], 'generators': [3, 2160, 36, 4466, 3552], 'label': '5832.gj.54.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '54.m1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956634
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.c1', '18.i1.a1'], 'contains': ['108.u2.b1', '108.bl1.b1', '108.bl1.e1', '162.j1.a1', '162.q1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1243, -1, 259, -1, 779, -1, 2443, -1], 'generators': [3, 2160, 36, 4466, 1608], 'label': '5832.gj.54.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '54.m1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956635
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '18.i1.a1'], 'contains': ['108.u2.c1', '108.bl1.c1', '108.bl1.f1', '162.j1.a1', '162.q1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1243, -1, 1222, -1, 779, -1, 1875, -1], 'generators': [3, 2160, 36, 4466, 5496], 'label': '5832.gj.54.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '54.m1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956636
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.l1.a1'], 'contains': ['108.x1.a1', '108.bm1.a1', '108.bm1.d1', '162.k1.a1', '162.q1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1367, -1, 1342, -1, 884, -1, 2154, -1], 'generators': [3, 2160, 36, 2232, 3552], 'label': '5832.gj.54.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '54.n1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956637
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '18.l1.a1'], 'contains': ['108.x1.b1', '108.bm1.b1', '108.bm1.e1', '162.k1.a1', '162.q1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1367, -1, 2031, -1, 884, -1, 2226, -1], 'generators': [3, 2160, 36, 2232, 5496], 'label': '5832.gj.54.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '54.n1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956638
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.c1', '18.l1.a1'], 'contains': ['108.x1.c1', '108.bm1.c1', '108.bm1.f1', '162.k1.a1', '162.q1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1367, -1, 1605, -1, 884, -1, 2646, -1], 'generators': [3, 2160, 36, 2232, 1608], 'label': '5832.gj.54.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '54.n1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956639
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.h1.a1', '18.k1.a1', '27.h1.a1'], 'contains': ['108.d1.a1', '108.bn1.a1', '108.bn1.b1', '162.l1.a1', '162.m1.a1', '162.n1.a1', '162.p1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6405, -1, 7659, -1, 5885, -1, 7291, -1], 'generators': [3, 1944, 36, 24, 216], 'label': '5832.gj.54.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.o1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956640
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.f2.a1', '18.i1.a1', '18.l1.a1'], 'contains': ['108.f1.a1', '108.bo1.a1', '108.bo1.b1', '162.l1.a1', '162.q1.a1', '162.q1.b1', '162.q1.c1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2043, -1, 1074, -1, 1564, -1, 2298, -1], 'generators': [3, 2160, 36, 3768, 1944], 'label': '5832.gj.54.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '54.p1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956641
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.a1', '18.j1.a1', '18.m1.a1', '27.i1.a1'], 'contains': ['108.h1.a1', '108.bp1.a1', '108.bp1.b1', '162.l1.a1', '162.o1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5875, -1, 6223, -1, 4759, -1, 6610, -1], 'generators': [3, 1944, 36, 3096, 216], 'label': '5832.gj.54.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.q1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956642
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '18.p1.a1', '18.r1.a1', '27.c1.a1'], 'contains': ['108.a1.a1', '162.r1.a1', '162.t1.a1', '162.ba1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8142, -1, 8999, -1, 8324, -1, 8405, -1], 'generators': [18, 1944, 578, 216, 36], 'label': '5832.gj.54.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.r1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956643
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '12.i1.a1', '12.i1.b1', '18.c1.a1', '18.e1.a1', '18.h1.a1', '18.k1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6476, -1, 6950, -1, 5041, -1, 6626, -1], 'generators': [3, 4104, 24, 36, 1944, 2, 288], 'label': '5832.gj.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956644
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1.a1', '18.q1.a1', '18.s1.a1', '27.c1.a1'], 'contains': ['108.a1.a1', '162.s1.a1', '162.u1.a1', '162.bb1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7889, -1, 8608, -1, 7182, -1, 8568, -1], 'generators': [21, 216, 578, 1944, 36], 'label': '5832.gj.54.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.s1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956645
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.n1.a1', '18.t1.a1', '18.u1.a1', '27.d1.a1'], 'contains': ['108.b1.a1', '162.r1.a1', '162.v1.a1', '162.bc1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8867, -1, 8364, -1, 8205, -1, 8730, -1], 'generators': [18, 1944, 216, 36, 504], 'label': '5832.gj.54.t1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.t1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956646
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.o1.a1', '18.v1.a1', '18.w1.a1', '27.d1.a1'], 'contains': ['108.b1.a1', '162.s1.a1', '162.w1.a1', '162.bd1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8598, -1, 7428, -1, 6801, -1, 9015, -1], 'generators': [21, 216, 1944, 36, 4176], 'label': '5832.gj.54.u1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.u1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.u1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956647
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.a1', '18.t1.a1', '27.h1.a1'], 'contains': ['108.d1.a1', '162.r1.a1', '162.x1.a1', '162.be1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9384, -1, 8773, -1, 9121, -1, 9404, -1], 'generators': [18, 1944, 24, 216, 36], 'label': '5832.gj.54.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.v1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 227956648
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.q1.a1', '27.h1.a1'], 'contains': ['108.d1.a1', '162.s1.a1', '162.y1.a1', '162.bf1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9223, -1, 8509, -1, 8442, -1, 9533, -1], 'generators': [21, 216, 1944, 36, 24], 'label': '5832.gj.54.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.w1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.w1.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 227956649
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.a1', '18.u1.a1'], 'contains': ['108.e1.a1', '162.r1.a1', '162.z1.a1', '162.bg1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9497, -1, 9563, -1, 9331, -1, 9323, -1], 'generators': [18, 1944, 602, 216, 36], 'label': '5832.gj.54.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1.a1', 'old_label': '54.x1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.x1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956650
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.r1.a1', '27.i1.a1'], 'contains': ['108.h1.a1', '162.r1.a1', '162.bh1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7429, -1, 8167, -1, 6539, -1, 7645, -1], 'generators': [18, 1944, 216, 36, 3096], 'label': '5832.gj.54.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.y1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.y1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 227956651
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1.a1', '18.v1.a1', '27.i1.a1'], 'contains': ['108.h1.a1', '162.s1.a1', '162.bi1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6992, -1, 7213, -1, 6243, -1, 7879, -1], 'generators': [21, 216, 1152, 36, 1944], 'label': '5832.gj.54.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.z1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.z1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 227956652
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1.a1', '18.w1.a1'], 'contains': ['108.i1.a1', '162.s1.a1', '162.bj1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7531, -1, 7290, -1, 6138, -1, 8023, -1], 'generators': [21, 216, 1082, 36, 1944], 'label': '5832.gj.54.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '54.ba1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956653
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '27.a1.a1'], 'contains': ['108.j1.a1', '162.t1.a1', '162.v1.a1', '162.bk1.a1', '162.bm1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8278, -1, 9197, -1, 8913, -1, 8182, -1], 'generators': [18, 4392, 2, 216, 36], 'label': '5832.gj.54.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.bb1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956654
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.e1.a1', '12.j1.a1', '12.j1.b1', '18.c1.a1', '18.d1.a1', '18.d1.b1', '18.d1.c1', '18.f1.a1', '18.f2.a1', '18.i1.a1', '18.l1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2149, -1, 1389, -1, 1789, -1, 2199, -1], 'generators': [3, 1944, 3768, 36, 2160, 2, 288], 'label': '5832.gj.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '6.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956655
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1.a1', '27.a1.a1'], 'contains': ['108.j1.a1', '162.u1.a1', '162.w1.a1', '162.bl1.a1', '162.bn1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7775, -1, 8688, -1, 7482, -1, 8649, -1], 'generators': [21, 216, 2, 36, 4392], 'label': '5832.gj.54.bc1.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': '54.bc1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956656
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.a1', '27.e1.a1'], 'contains': ['108.k1.a1', '162.t1.a1', '162.x1.a1', '162.z1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9875, -1, 9680, -1, 9558, -1, 9616, -1], 'generators': [18, 216, 2522, 24, 36], 'label': '5832.gj.54.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '54.bd1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956657
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.a1'], 'contains': ['108.k2.a1', '162.u1.a1', '162.y1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9598, -1, 9419, -1, 8707, -1, 9689, -1], 'generators': [21, 216, 578, 36, 24], 'label': '5832.gj.54.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '54.be1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.be1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956658
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.be2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.a1', '27.e1.a1'], 'contains': ['108.k1.a1', '162.u1.a1', '162.y1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9685, -1, 9487, -1, 9226, -1, 9750, -1], 'generators': [21, 216, 2522, 36, 24], 'label': '5832.gj.54.be2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.be2.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.be2.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956659
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '27.b1.a1'], 'contains': ['108.l1.a1', '162.ba1.a1', '162.bc1.a1', '162.bk1.a1', '162.bm1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8392, -1, 9268, -1, 7983, -1, 8100, -1], 'generators': [18, 1944, 2, 36, 4392], 'label': '5832.gj.54.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.bf1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956660
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1.a1', '27.b1.a1'], 'contains': ['108.l1.a1', '162.bb1.a1', '162.bd1.a1', '162.bl1.a1', '162.bn1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7638, -1, 8872, -1, 7300, -1, 8486, -1], 'generators': [21, 4392, 2, 1944, 36], 'label': '5832.gj.54.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.bg1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956661
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1.a1'], 'contains': ['108.m2.a1', '162.ba1.a1', '162.bh1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7343, -1, 8423, -1, 6704, -1, 7758, -1], 'generators': [18, 1944, 578, 36, 1152], 'label': '5832.gj.54.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1.a1', 'old_label': '54.bh1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956662
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1.a1', '27.f1.a1'], 'contains': ['108.m1.a1', '162.ba1.a1', '162.bh1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7270, -1, 8307, -1, 6629, -1, 7706, -1], 'generators': [18, 1944, 2306, 36, 1152], 'label': '5832.gj.54.bh2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.bh2.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bh2.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956663
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1.a1', '27.f1.a1'], 'contains': ['108.m1.a1', '162.bb1.a1', '162.bi1.a1', '162.bj1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7138, -1, 7951, -1, 6348, -1, 7951, -1], 'generators': [21, 1944, 2306, 5040, 36], 'label': '5832.gj.54.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '54.bi1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956664
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.t1.a1', '27.g1.a1'], 'contains': ['108.n1.a1', '162.bc1.a1', '162.be1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8967, -1, 8023, -1, 8546, -1, 9207, -1], 'generators': [18, 1944, 24, 36, 4392], 'label': '5832.gj.54.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '54.bj1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956665
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.a1'], 'contains': ['12.b1.a1', '12.k1.a1', '12.k1.b1', '18.c1.a1', '18.g1.a1', '18.j1.a1', '18.m1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5880, -1, 6013, -1, 4462, -1, 6383, -1], 'generators': [3, 4104, 3096, 36, 1944, 2, 288], 'label': '5832.gj.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956666
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '27.g1.a1'], 'contains': ['108.n1.a1', '162.bd1.a1', '162.bf1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8686, -1, 7900, -1, 7391, -1, 9260, -1], 'generators': [21, 1944, 36, 24, 4176], 'label': '5832.gj.54.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.g1.a1', 'old_label': '54.bk1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956667
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '54.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.u1.a1'], 'contains': ['108.o1.a1', '162.bc1.a1', '162.bg1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9054, -1, 9344, -1, 9017, -1, 8872, -1], 'generators': [18, 1944, 26, 36, 2448], 'label': '5832.gj.54.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1.a1', 'old_label': '54.bl1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956668
    {'ambient': '5832.gj', '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': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.d1.a1', '36.a1.a1', '36.p1.a1', '36.p1.b1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.j1.a1', '216.l1.a1', '216.p1.a1', '216.t1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3314, 5352, 5330, 3112, 3018, 5811, 4672, 5789], 'generators': [2, 288, 216, 1944], 'label': '5832.gj.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1'], 'normal_contains': ['216.a1.a1', '216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '36.10', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956669
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.c1.a1', '24.e1.a1', '36.b1.a1', '36.x1.a1', '36.x1.b1'], 'contains': ['216.b1.a1', '216.d1.a1', '216.n1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5353, 4121, 5612, 4514, 3952, 4727, 6293, 4823], 'generators': [24, 288, 216], 'label': '5832.gj.72.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.a1.a1', '24.c1.a1', '36.b1.a1'], 'normal_contains': ['216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '5832.gj', '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': '324.117'}
  • id: 227956670
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '24.g1.a1', '36.c1.a1', '36.z1.a1', '36.z1.b1'], 'contains': ['216.b1.a1', '216.h1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4377, 2755, 4993, 2291, 2886, 3352, 5778, 3753], 'generators': [1152, 288], 'label': '5832.gj.72.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.c1.a1', 'normal_contained_in': ['24.b1.a1', '24.c1.a1', '36.c1.a1'], 'normal_contains': ['216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '5832.gj', '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': '324.117'}
  • id: 227956671
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.d1.a1', '36.r1.a1', '36.r1.b1'], 'contains': ['216.c1.a1', '216.d1.a1', '216.e1.a1', '216.r1.a1', '216.v1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4214, -1, 6119, -1, 4137, -1, 5038, -1], 'generators': [2, 24, 1944], 'label': '5832.gj.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.d1.a1', 'projective_image': '5832.gj', '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': '54.12'}
  • id: 227956672
    {'ambient': '5832.gj', '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': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.e1.a1', '36.s1.a1', '36.s1.b1'], 'contains': ['216.c1.a1', '216.f1.a1', '216.g1.a1', '216.q1.a1', '216.q1.b1', '216.q1.c1', '216.q2.a1', '216.q2.b1', '216.q2.c1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [776, -1, 2665, -1, 1463, -1, 391, -1], 'generators': [2, 1464, 1944], 'label': '5832.gj.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '72.e1.a1', 'projective_image': '5832.gj', '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': '6.2'}
  • id: 227956673
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.e2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.e2.a1', '36.s2.a1', '36.s2.b1'], 'contains': ['216.c1.a1', '216.f1.a1', '216.g1.a1', '216.s1.a1', '216.s1.b1', '216.s1.c1', '216.w1.a1', '216.w1.b1', '216.w1.c1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [920, -1, 2561, -1, 1565, -1, 533, -1], 'generators': [290, 1464, 1944], 'label': '5832.gj.72.e2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '72.e2.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e2.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956674
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.f1.a1', '36.t1.a1', '36.t1.b1'], 'contains': ['216.c1.a1', '216.h1.a1', '216.i1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4446, -1, 5108, -1, 2957, -1, 5867, -1], 'generators': [2, 1152], 'label': '5832.gj.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '72.f1.a1', 'projective_image': '5832.gj', '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': '54.12'}
  • id: 227956675
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.g1.a1', '36.u1.a1', '36.u1.b1'], 'contains': ['216.a1.a1', '216.d1.a1', '216.e1.a1', '216.k1.a1', '216.k2.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5611, -1, 6912, -1, 5516, -1, 7042, -1], 'generators': [578, 24, 1944], 'label': '5832.gj.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.g1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 227956676
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.a1.a1', '18.n1.a1', '18.p1.a1', '18.t1.a1', '18.u1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8486, -1, 8491, -1, 7919, -1, 8429, -1], 'generators': [18, 4392, 4104, 2, 1944, 24, 36], 'label': '5832.gj.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
  • id: 227956677
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.h1.a1', '36.v1.a1', '36.v1.b1'], 'contains': ['216.a1.a1', '216.f1.a1', '216.g1.a1', '216.u1.a1', '216.u1.b1', '216.u1.c1', '216.u2.a1', '216.u2.b1', '216.u2.c1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2125, -1, 2418, -1, 1670, -1, 249, -1], 'generators': [578, 1464, 1944], 'label': '5832.gj.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '72.h1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956678
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.i1.a1', '36.w1.a1', '36.w1.b1'], 'contains': ['216.a1.a1', '216.h1.a1', '216.i1.a1', '216.m1.a1', '216.m2.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4876, -1, 5893, -1, 3562, -1, 6092, -1], 'generators': [578, 1152, 216], 'label': '5832.gj.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.i1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 227956679
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.f1.a1', '24.g1.a1', '36.j1.a1'], 'contains': ['216.b1.a1', '216.e1.a1', '216.o1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5470, -1, 5524, -1, 3831, -1, 6210, -1], 'generators': [26, 288, 216], 'label': '5832.gj.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.j1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
  • id: 227956680
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.f1.a1', '36.k1.a1', '36.y1.a1', '36.y1.b1'], 'contains': ['216.b1.a1', '216.f1.a1', '216.x1.a1', '216.x1.b1', '216.x1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2410, -1, 4226, -1, 1980, -1, 1075, -1], 'generators': [1464, 288, 1944], 'label': '5832.gj.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.k1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 227956681
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1', '36.l1.a1'], 'contains': ['216.b1.a1', '216.g1.a1', '216.y1.a1', '216.y1.b1', '216.y1.c1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3013, -1, 4883, -1, 2085, -1, 2019, -1], 'generators': [1178, 288, 1944], 'label': '5832.gj.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.l1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 227956682
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.e1.a1', '24.f1.a1', '36.m1.a1'], 'contains': ['216.b1.a1', '216.i1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4514, -1, 5150, -1, 2815, -1, 5916, -1], 'generators': [1154, 288], 'label': '5832.gj.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '72.m1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
  • id: 227956683
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.n1.a1'], 'contains': ['216.p1.a1', '216.q1.a1', '216.q1.b1', '216.q2.b1', '216.u1.a1', '216.u1.b1', '216.u2.b1', '216.w1.a1', '216.w1.b1', '216.x1.a1', '216.y1.a1', '216.y1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [538, -1, 3317, -1, 468, -1, 461, -1], 'generators': [2, 1464, 288], 'label': '5832.gj.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '72.n1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956684
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.n1.b1'], 'contains': ['216.p1.a1', '216.q1.a1', '216.q1.c1', '216.q2.a1', '216.u1.a1', '216.u1.c1', '216.u2.a1', '216.w1.a1', '216.w1.c1', '216.x1.b1', '216.y1.a1', '216.y1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [538, -1, 3472, -1, 468, -1, 177, -1], 'generators': [2, 3408, 288], 'label': '5832.gj.72.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '72.n1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956685
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.n1.c1'], 'contains': ['216.p1.a1', '216.q1.b1', '216.q1.c1', '216.q2.c1', '216.u1.b1', '216.u1.c1', '216.u2.c1', '216.w1.b1', '216.w1.c1', '216.x1.c1', '216.y1.b1', '216.y1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [538, -1, 3572, -1, 468, -1, 104, -1], 'generators': [2, 5352, 288], 'label': '5832.gj.72.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '72.n1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956686
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.o1.a1', '36.q1.a1', '36.q1.d1'], 'contains': ['216.q1.b1', '216.q2.a1', '216.s1.a1', '216.s1.b1', '216.t1.a1', '216.u1.b1', '216.u2.a1', '216.x1.a1', '216.y1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [366, -1, 1067, -1, 307, -1, 32, -1], 'generators': [1946, 1464, 288], 'label': '5832.gj.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '72.o1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956687
    {'ambient': '5832.gj', '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': '2916.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '6.a1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6016, 1790, 5990, 3023, 4268, 1458, 6336, 3151], 'generators': [3, 3096, 288, 36, 24, 1944, 216, 2], 'label': '5832.gj.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2916.ef'}
  • id: 227956688
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.c1.a1'], 'contains': ['12.b1.a1', '18.o1.a1', '18.s1.a1', '18.v1.a1', '18.w1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7408, -1, 7474, -1, 6117, -1, 7971, -1], 'generators': [21, 4392, 1944, 2, 216, 1152, 36], 'label': '5832.gj.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.j1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
  • id: 227956689
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.o1.b1', '36.q1.b1', '36.q1.e1'], 'contains': ['216.q1.a1', '216.q2.c1', '216.s1.a1', '216.s1.c1', '216.t1.a1', '216.u1.a1', '216.u2.c1', '216.x1.b1', '216.y1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [366, -1, 2119, -1, 307, -1, 321, -1], 'generators': [1946, 3408, 288], 'label': '5832.gj.72.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '72.o1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956690
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.o1.c1', '36.q1.c1', '36.q1.f1'], 'contains': ['216.q1.c1', '216.q2.b1', '216.s1.b1', '216.s1.c1', '216.t1.a1', '216.u1.c1', '216.u2.b1', '216.x1.c1', '216.y1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [366, -1, 1943, -1, 307, -1, 605, -1], 'generators': [1946, 5352, 288], 'label': '5832.gj.72.o1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '72.o1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956691
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1'], 'contains': ['162.a1.a1', '162.bk1.a1', '162.bl1.a1', '243.a1.a1', '243.b1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8028, -1, 9193, -1, 7800, -1, 8328, -1], 'generators': [3, 4392, 18, 2, 36], 'label': '5832.gj.81.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '81.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956692
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.c1.a1', '27.e1.a1'], 'contains': ['162.c1.a1', '162.t1.a1', '162.u1.a1', '243.a1.a1', '243.c1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8151, -1, 9256, -1, 8803, -1, 8806, -1], 'generators': [3, 216, 18, 2522, 36], 'label': '5832.gj.81.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1.a1', 'old_label': '81.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956693
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '81.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.d1.a1'], 'contains': ['162.d1.a1', '162.v1.a1', '162.w1.a1', '243.b1.a1', '243.c1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8688, -1, 8827, -1, 8094, -1, 9092, -1], 'generators': [3, 216, 18, 36, 4392], 'label': '5832.gj.81.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '81.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956694
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '81.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.b1.a1', '27.c1.a1', '27.f1.a1'], 'contains': ['162.f1.a1', '162.ba1.a1', '162.bb1.a1', '243.a1.a1', '243.d1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [7837, -1, 8989, -1, 7592, -1, 8257, -1], 'generators': [3, 1944, 18, 2306, 36], 'label': '5832.gj.81.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.d1.a1', 'old_label': '81.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956695
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '81.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.b1.a1', '27.d1.a1', '27.g1.a1'], 'contains': ['162.g1.a1', '162.bc1.a1', '162.bd1.a1', '243.b1.a1', '243.d1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8811, -1, 8217, -1, 7695, -1, 8939, -1], 'generators': [3, 1944, 18, 36, 4392], 'label': '5832.gj.81.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '81.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956696
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '81.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.c1.a1', '27.d1.a1', '27.h1.a1', '27.i1.a1'], 'contains': ['162.l1.a1', '162.r1.a1', '162.s1.a1', '243.c1.a1', '243.d1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8965, -1, 8498, -1, 7888, -1, 9152, -1], 'generators': [3, 1944, 18, 36, 216], 'label': '5832.gj.81.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '81.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956697
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '81.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.e1.a1', '27.h1.a1'], 'contains': ['162.m1.a1', '162.x1.a1', '162.y1.a1', '243.c1.a1', '243.e1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9813, -1, 9523, -1, 9441, -1, 9817, -1], 'generators': [3, 216, 18, 36, 24], 'label': '5832.gj.81.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '81.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.g1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956698
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '81.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.g1.a1', '27.h1.a1'], 'contains': ['162.n1.a1', '162.be1.a1', '162.bf1.a1', '243.d1.a1', '243.e1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9309, -1, 8270, -1, 8626, -1, 9469, -1], 'generators': [3, 1944, 18, 36, 24], 'label': '5832.gj.81.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.h1.a1', 'old_label': '81.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956699
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['12.f1.a1', '18.a1.a1', '18.w1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7624, -1, 7412, -1, 5905, -1, 8042, -1], 'generators': [21, 216, 3960, 1154, 1944, 36, 24], 'label': '5832.gj.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '6.k1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': '486.127'}
  • id: 227956700
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '81.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.f1.a1', '27.i1.a1'], 'contains': ['162.o1.a1', '162.bh1.a1', '162.bi1.a1', '243.d1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7033, -1, 7989, -1, 6444, -1, 7813, -1], 'generators': [3, 1944, 18, 36, 1152], 'label': '5832.gj.81.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '81.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.i1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956701
    {'ambient': '5832.gj', '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': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.g1.a1', '36.h1.a1', '36.i1.a1', '54.e1.a1', '54.r1.a1', '54.s1.a1'], 'contains': ['216.a1.a1', '324.a1.a1', '324.c1.a1', '324.h1.a1', '324.p1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5602, 7817, 7287, 6028, 5406, 7988, 7117, 7881], 'generators': [36, 578, 216, 1944], 'label': '5832.gj.108.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1'], 'normal_contains': ['216.a1.a1', '324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '36.10', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956702
    {'ambient': '5832.gj', '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': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '36.j1.a1', '36.k1.a1', '36.l1.a1', '36.m1.a1', '54.f1.a1', '54.t1.a1', '54.u1.a1'], 'contains': ['216.b1.a1', '324.a1.a1', '324.d1.a1', '324.i1.a1', '324.r1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6556, 6415, 6961, 4777, 4760, 6755, 6966, 6782], 'generators': [36, 288, 216, 1944], 'label': '5832.gj.108.b1.a1', 'mobius_quo': 0, 'mobius_sub': -18, 'normal_closure': '108.b1.a1', 'normal_contained_in': ['36.a1.a1', '36.b1.a1', '36.c1.a1'], 'normal_contains': ['216.b1.a1', '324.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '36.10', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956703
    {'ambient': '5832.gj', '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': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.d1.a1', '36.e1.a1', '36.e2.a1', '36.f1.a1', '54.d1.a1'], 'contains': ['216.c1.a1', '324.a1.a1', '324.b1.a1', '324.g1.a1', '324.n1.a1', '324.o1.a1', '324.q1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3390, -1, 5759, -1, 3297, -1, 5531, -1], 'generators': [36, 2, 216, 1944], 'label': '5832.gj.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '2916.ef', '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': '6.1'}
  • id: 227956704
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.d1.a1', '36.g1.a1', '54.o1.a1', '54.v1.a1', '54.w1.a1'], 'contains': ['216.d1.a1', '324.a1.a1', '324.e1.a1', '324.j1.a1', '324.s1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6961, -1, 8036, -1, 6397, -1, 7776, -1], 'generators': [36, 24, 216, 1944], 'label': '5832.gj.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 227956705
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.g1.a1', '36.j1.a1', '54.x1.a1'], 'contains': ['216.e1.a1', '324.a1.a1', '324.f1.a1', '324.k1.a1', '324.t1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7104, -1, 7762, -1, 6298, -1, 7481, -1], 'generators': [36, 26, 216, 1944], 'label': '5832.gj.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '108.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956706
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.e2.a1', '36.h1.a1', '36.k1.a1', '54.p1.a1'], 'contains': ['216.f1.a1', '324.a1.a1', '324.u1.a1', '324.u1.b1', '324.u1.c1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2230, -1, 3221, -1, 1774, -1, 2517, -1], 'generators': [36, 1464, 1944, 2160], 'label': '5832.gj.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956707
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.e2.a1', '36.h1.a1', '36.l1.a1'], 'contains': ['216.g1.a1', '324.a1.a1', '324.v1.a1', '324.v1.b1', '324.v1.c1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2375, -1, 4375, -1, 1876, -1, 3591, -1], 'generators': [36, 1178, 1944, 4104], 'label': '5832.gj.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956708
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.f1.a1', '36.i1.a1', '54.q1.a1', '54.y1.a1', '54.z1.a1'], 'contains': ['216.h1.a1', '324.a1.a1', '324.l1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6179, -1, 6825, -1, 5201, -1, 7341, -1], 'generators': [36, 1152, 216, 1944], 'label': '5832.gj.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 227956709
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.i1.a1', '36.m1.a1', '54.ba1.a1'], 'contains': ['216.i1.a1', '324.a1.a1', '324.m1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6277, -1, 6900, -1, 4659, -1, 7412, -1], 'generators': [36, 1154, 216, 1944], 'label': '5832.gj.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '108.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956710
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.h1.a1', '18.b1.a1', '18.u1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7857, -1, 8294, -1, 6756, -1, 7457, -1], 'generators': [18, 216, 2448, 26, 1944, 36, 3096], 'label': '5832.gj.6.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '6.l1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1.a1', 'subgroup_fusion': None, 'weyl_group': '486.129'}
  • id: 227956711
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.a1.a1', '54.bb1.a1', '54.bc1.a1'], 'contains': ['216.j1.a1', '324.b1.a1', '324.c1.a1', '324.d1.a1', '324.w1.a1', '324.x1.a1', '324.y1.a1', '324.y2.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5227, -1, 8555, -1, 6495, -1, 7185, -1], 'generators': [36, 2, 288, 216], 'label': '5832.gj.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.j1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 227956712
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '54.g1.a1', '54.bd1.a1', '54.be2.a1'], 'contains': ['216.k1.a1', '324.c1.a1', '324.e1.a1', '324.f1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9659, -1, 9798, -1, 8977, -1, 9032, -1], 'generators': [36, 2306, 24, 216], 'label': '5832.gj.108.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.k1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956713
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '54.be1.a1'], 'contains': ['216.k2.a1', '324.c1.a1', '324.e1.a1', '324.f1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9518, -1, 9437, -1, 8157, -1, 9115, -1], 'generators': [36, 362, 24, 216], 'label': '5832.gj.108.k2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '108.k2.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k2.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956714
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '54.b1.a1', '54.bf1.a1', '54.bg1.a1'], 'contains': ['216.l1.a1', '324.g1.a1', '324.h1.a1', '324.i1.a1', '324.w1.a1', '324.x1.a1', '324.y1.a1', '324.y2.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5322, -1, 8615, -1, 6114, -1, 6898, -1], 'generators': [36, 2, 288, 1944], 'label': '5832.gj.108.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.l1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 227956715
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '54.h1.a1', '54.bh2.a1', '54.bi1.a1'], 'contains': ['216.m1.a1', '324.h1.a1', '324.l1.a1', '324.m1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5770, -1, 7933, -1, 5686, -1, 7551, -1], 'generators': [36, 2306, 5040, 1944], 'label': '5832.gj.108.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.m1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956716
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.m2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '54.bh1.a1'], 'contains': ['216.m2.a1', '324.h1.a1', '324.l1.a1', '324.m1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5871, -1, 7592, -1, 5791, -1, 7623, -1], 'generators': [36, 2522, 5040, 1944], 'label': '5832.gj.108.m2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1.a1', 'old_label': '108.m2.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m2.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956717
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '54.i1.a1', '54.bj1.a1', '54.bk1.a1'], 'contains': ['216.n1.a1', '324.i1.a1', '324.j1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7348, -1, 7481, -1, 6754, -1, 7852, -1], 'generators': [36, 24, 288, 1944], 'label': '5832.gj.108.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '108.n1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956718
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '54.bl1.a1'], 'contains': ['216.o1.a1', '324.i1.a1', '324.k1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7512, -1, 8418, -1, 6875, -1, 7701, -1], 'generators': [36, 26, 4176, 1944], 'label': '5832.gj.108.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1.a1', 'old_label': '108.o1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956719
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.n1.a1', '36.n1.b1', '36.n1.c1'], 'contains': ['216.p1.a1', '324.n1.a1', '324.p1.a1', '324.q1.a1', '324.r1.a1', '324.w1.a1', '324.y1.a1', '324.y2.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3271, -1, 4868, -1, 3198, -1, 4576, -1], 'generators': [36, 1946, 288, 4104], 'label': '5832.gj.108.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.p1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956720
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.n1.a1', '36.n1.b1', '36.o1.b1'], 'contains': ['216.q1.a1', '324.n1.a1', '324.u1.a1', '324.v1.b1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1199, -1, 4127, -1, 989, -1, 3234, -1], 'generators': [36, 2, 5784, 2160], 'label': '5832.gj.108.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.q1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956721
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': ['729.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4573, 2264, 5063, 1015, 3060, 2173, 5449, 3033], 'generators': [2, 24, 1152], 'label': '5832.gj.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'normal_contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
  • id: 227956722
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.n1.a1', '36.n1.c1', '36.o1.a1'], 'contains': ['216.q1.b1', '324.n1.a1', '324.u1.b1', '324.v1.a1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1199, -1, 4065, -1, 989, -1, 3163, -1], 'generators': [36, 2, 3840, 2160], 'label': '5832.gj.108.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.q1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956723
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.n1.b1', '36.n1.c1', '36.o1.c1'], 'contains': ['216.q1.c1', '324.n1.a1', '324.u1.c1', '324.v1.a1', '324.v1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1199, -1, 4314, -1, 989, -1, 3662, -1], 'generators': [36, 2, 1896, 2160], 'label': '5832.gj.108.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.q1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956724
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.q2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.n1.b1', '36.o1.a1', '54.j1.a1'], 'contains': ['216.q2.a1', '324.n1.a1', '324.u1.a1', '324.v1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [851, -1, 2466, -1, 572, -1, 2230, -1], 'generators': [36, 1946, 5784, 2160], 'label': '5832.gj.108.q2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.q2.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q2.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956725
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.q2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.n1.a1', '36.o1.c1', '54.j1.b1'], 'contains': ['216.q2.b1', '324.n1.a1', '324.u1.b1', '324.v1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [851, -1, 2720, -1, 572, -1, 3448, -1], 'generators': [36, 1946, 3840, 2160], 'label': '5832.gj.108.q2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.q2.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q2.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956726
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.q2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.n1.c1', '36.o1.b1', '54.j1.c1'], 'contains': ['216.q2.c1', '324.n1.a1', '324.u1.c1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [851, -1, 3865, -1, 572, -1, 2660, -1], 'generators': [36, 1946, 1896, 2160], 'label': '5832.gj.108.q2.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.q2.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q2.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956727
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '54.k1.a1'], 'contains': ['216.r1.a1', '324.o1.a1', '324.s1.a1', '324.t1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4012, -1, 7041, -1, 4357, -1, 4732, -1], 'generators': [36, 2, 24, 4104], 'label': '5832.gj.108.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '108.r1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956728
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e2.a1', '36.o1.a1', '36.o1.b1', '54.l1.a1'], 'contains': ['216.s1.a1', '324.o1.a1', '324.u1.a1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [975, -1, 3031, -1, 675, -1, 2374, -1], 'generators': [36, 2234, 5784, 2160], 'label': '5832.gj.108.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.s1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956729
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e2.a1', '36.o1.a1', '36.o1.c1', '54.l1.b1'], 'contains': ['216.s1.b1', '324.o1.a1', '324.u1.b1', '324.v1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [975, -1, 2207, -1, 675, -1, 2803, -1], 'generators': [36, 2234, 3840, 2160], 'label': '5832.gj.108.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.s1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956730
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e2.a1', '36.o1.b1', '36.o1.c1', '54.l1.c1'], 'contains': ['216.s1.c1', '324.o1.a1', '324.u1.c1', '324.v1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [975, -1, 2954, -1, 675, -1, 2731, -1], 'generators': [36, 2234, 1896, 2160], 'label': '5832.gj.108.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.s1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956731
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.o1.a1', '36.o1.b1', '36.o1.c1', '54.c1.a1'], 'contains': ['216.t1.a1', '324.n1.a1', '324.o1.a1', '324.p1.a1', '324.r1.a1', '324.w1.a1', '324.x1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3058, -1, 2617, -1, 2730, -1, 4321, -1], 'generators': [36, 2, 288, 4104], 'label': '5832.gj.108.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.t1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956732
    {'ambient': '5832.gj', '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': '972.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '3.c1.a1'], 'contains': ['18.c1.a1', '18.n1.a1', '18.o1.a1', '27.a1.a1', '27.b1.a1', '27.c1.a1', '27.d1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8021, -1, 8431, -1, 7309, -1, 8345, -1], 'generators': [3, 216, 4392, 18, 1944, 2, 36], 'label': '5832.gj.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': '2916.ef', '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': '108.40'}
  • id: 227956733
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.a1', '36.n1.b1', '36.o1.b1'], 'contains': ['216.u1.a1', '324.p1.a1', '324.u1.a1', '324.v1.b1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1423, -1, 4189, -1, 1093, -1, 3020, -1], 'generators': [36, 578, 5784, 2160], 'label': '5832.gj.108.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.u1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956734
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.a1', '36.n1.c1', '36.o1.a1'], 'contains': ['216.u1.b1', '324.p1.a1', '324.u1.b1', '324.v1.a1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1423, -1, 3927, -1, 1093, -1, 2948, -1], 'generators': [36, 578, 3840, 2160], 'label': '5832.gj.108.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.u1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956735
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.b1', '36.n1.c1', '36.o1.c1'], 'contains': ['216.u1.c1', '324.p1.a1', '324.u1.c1', '324.v1.a1', '324.v1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1423, -1, 4252, -1, 1093, -1, 3377, -1], 'generators': [36, 578, 1896, 2160], 'label': '5832.gj.108.u1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.u1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956736
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.b1', '36.o1.a1', '54.m1.a1'], 'contains': ['216.u2.a1', '324.p1.a1', '324.u1.a1', '324.v1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1076, -1, 2327, -1, 780, -1, 2159, -1], 'generators': [36, 2522, 5784, 2160], 'label': '5832.gj.108.u2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.u2.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u2.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956737
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.a1', '36.o1.c1', '54.m1.b1'], 'contains': ['216.u2.b1', '324.p1.a1', '324.u1.b1', '324.v1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1076, -1, 2403, -1, 780, -1, 3092, -1], 'generators': [36, 2522, 3840, 2160], 'label': '5832.gj.108.u2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.u2.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u2.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956738
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.c1', '36.o1.b1', '54.m1.c1'], 'contains': ['216.u2.c1', '324.p1.a1', '324.u1.c1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1076, -1, 3803, -1, 780, -1, 2589, -1], 'generators': [36, 2522, 1896, 2160], 'label': '5832.gj.108.u2.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.u2.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u2.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956739
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1'], 'contains': ['216.v1.a1', '324.q1.a1', '324.s1.a1', '324.t1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4323, -1, 7177, -1, 4870, -1, 4815, -1], 'generators': [36, 1946, 24, 4104], 'label': '5832.gj.108.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '108.v1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956740
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e2.a1', '36.n1.a1', '36.n1.b1'], 'contains': ['216.w1.a1', '324.q1.a1', '324.u1.a1', '324.v1.a1', '324.v1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1546, -1, 4437, -1, 1303, -1, 3733, -1], 'generators': [36, 290, 5784, 2160], 'label': '5832.gj.108.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.w1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956741
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e2.a1', '36.n1.a1', '36.n1.c1'], 'contains': ['216.w1.b1', '324.q1.a1', '324.u1.b1', '324.v1.b1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1546, -1, 4500, -1, 1303, -1, 3805, -1], 'generators': [36, 290, 3840, 2160], 'label': '5832.gj.108.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.w1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956742
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e2.a1', '36.n1.b1', '36.n1.c1'], 'contains': ['216.w1.c1', '324.q1.a1', '324.u1.c1', '324.v1.a1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1546, -1, 4639, -1, 1303, -1, 3305, -1], 'generators': [36, 290, 1896, 2160], 'label': '5832.gj.108.w1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.w1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956743
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.h1.a1', '18.p1.a1', '18.q1.a1', '27.c1.a1', '27.e1.a1', '27.h1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8946, -1, 8570, -1, 8191, -1, 9050, -1], 'generators': [3, 4104, 24, 18, 1944, 578, 36], 'label': '5832.gj.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
  • id: 227956744
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '36.n1.a1', '36.o1.a1', '54.n1.a1'], 'contains': ['216.x1.a1', '324.r1.a1', '324.u1.a1', '324.u1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1322, -1, 2542, -1, 885, -1, 2302, -1], 'generators': [36, 1464, 2448, 2160], 'label': '5832.gj.108.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.x1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956745
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '36.n1.b1', '36.o1.b1', '54.n1.b1'], 'contains': ['216.x1.b1', '324.r1.a1', '324.u1.a1', '324.u1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1322, -1, 3990, -1, 885, -1, 2446, -1], 'generators': [36, 3408, 2448, 2160], 'label': '5832.gj.108.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.x1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956746
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '36.n1.c1', '36.o1.c1', '54.n1.c1'], 'contains': ['216.x1.c1', '324.r1.a1', '324.u1.b1', '324.u1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1322, -1, 3726, -1, 885, -1, 2875, -1], 'generators': [36, 5352, 2448, 2160], 'label': '5832.gj.108.x1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.x1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956747
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.n1.a1', '36.n1.b1', '36.o1.c1'], 'contains': ['216.y1.a1', '324.r1.a1', '324.v1.a1', '324.v1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2107, -1, 4576, -1, 1198, -1, 3949, -1], 'generators': [36, 3122, 288, 4104], 'label': '5832.gj.108.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.y1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956748
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.n1.b1', '36.n1.c1', '36.o1.a1'], 'contains': ['216.y1.b1', '324.r1.a1', '324.v1.a1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2107, -1, 4793, -1, 1198, -1, 3520, -1], 'generators': [36, 1178, 288, 4104], 'label': '5832.gj.108.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.y1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956749
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.n1.a1', '36.n1.c1', '36.o1.b1'], 'contains': ['216.y1.c1', '324.r1.a1', '324.v1.b1', '324.v1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2107, -1, 4716, -1, 1198, -1, 3877, -1], 'generators': [36, 5066, 288, 4104], 'label': '5832.gj.108.y1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '108.y1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956750
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '54.a1.a1'], 'contains': ['216.j1.a1', '324.z1.a1', '324.ba1.a1', '324.bb1.a1', '324.bc1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3176, -1, 6677, -1, 4247, -1, 5392, -1], 'generators': [39, 2, 4392, 216], 'label': '5832.gj.108.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.z1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956751
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.b1', '54.a1.a1'], 'contains': ['216.j1.a1', '324.z1.b1', '324.ba1.b1', '324.bb1.b1', '324.bc1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3176, -1, 6263, -1, 4247, -1, 5113, -1], 'generators': [3, 2, 4392, 216], 'label': '5832.gj.108.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.z1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956752
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '54.b1.a1'], 'contains': ['216.l1.a1', '324.z1.a1', '324.bd1.a1', '324.be1.a1', '324.bf1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2917, -1, 6735, -1, 3721, -1, 5181, -1], 'generators': [39, 2, 4392, 1944], 'label': '5832.gj.108.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '108.ba1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956753
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.b1', '54.b1.a1'], 'contains': ['216.l1.a1', '324.z1.b1', '324.bd1.b1', '324.be1.b1', '324.bf1.b1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2917, -1, 6364, -1, 3721, -1, 4890, -1], 'generators': [3, 2, 4392, 1944], 'label': '5832.gj.108.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '108.ba1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956754
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['18.j1.a1', '18.r1.a1', '18.s1.a1', '27.c1.a1', '27.f1.a1', '27.i1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7427, -1, 8096, -1, 6402, -1, 7799, -1], 'generators': [3, 4104, 3096, 18, 1944, 578, 36], 'label': '5832.gj.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 227956755
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '36.q1.a1', '36.q1.b1', '36.q1.c1', '54.c1.a1'], 'contains': ['216.t1.a1', '324.z1.a1', '324.bg1.a1', '324.bh1.a1', '324.bi1.a1', '324.bj1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1644, -1, 1237, -1, 2187, -1, 4019, -1], 'generators': [39, 2, 4392, 4104], 'label': '5832.gj.108.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '108.bb1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956756
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.b1', '36.q1.d1', '36.q1.e1', '36.q1.f1', '54.c1.a1'], 'contains': ['216.t1.a1', '324.z1.b1', '324.bg1.b1', '324.bh1.b1', '324.bi1.b1', '324.bj1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1644, -1, 266, -1, 2187, -1, 2089, -1], 'generators': [3, 2, 4392, 4104], 'label': '5832.gj.108.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '108.bb1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956757
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '36.r1.a1', '36.s1.a1', '36.s2.a1', '36.t1.a1', '54.d1.a1'], 'contains': ['216.c1.a1', '324.ba1.a1', '324.bd1.a1', '324.bg1.a1', '324.bh1.a1', '324.bk1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1834, -1, 5422, -1, 2543, -1, 4506, -1], 'generators': [39, 2, 216, 1944], 'label': '5832.gj.108.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '108.bc1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 227956758
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.b1', '36.r1.b1', '36.s1.b1', '36.s2.b1', '36.t1.b1', '54.d1.a1'], 'contains': ['216.c1.a1', '324.ba1.b1', '324.bd1.b1', '324.bg1.b1', '324.bh1.b1', '324.bk1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1834, -1, 5000, -1, 2543, -1, 4391, -1], 'generators': [3, 2, 216, 1944], 'label': '5832.gj.108.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '108.bc1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 227956759
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '36.u1.a1', '36.v1.a1', '36.w1.a1', '54.e1.a1'], 'contains': ['216.a1.a1', '324.bb1.a1', '324.be1.a1', '324.bi1.a1', '324.bk1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3518, -1, 5841, -1, 3457, -1, 5461, -1], 'generators': [39, 578, 4104, 1944], 'label': '5832.gj.108.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.bd1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956760
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.b1', '36.u1.b1', '36.v1.b1', '36.w1.b1', '54.e1.a1'], 'contains': ['216.a1.a1', '324.bb1.b1', '324.be1.b1', '324.bi1.b1', '324.bk1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3518, -1, 5621, -1, 3457, -1, 5250, -1], 'generators': [3, 578, 4104, 1944], 'label': '5832.gj.108.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.bd1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956761
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '36.x1.a1', '36.y1.a1', '36.z1.a1', '54.f1.a1'], 'contains': ['216.b1.a1', '324.bc1.a1', '324.bf1.a1', '324.bj1.a1', '324.bk1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3666, -1, 5697, -1, 3096, -1, 5322, -1], 'generators': [39, 288, 4104, 1944], 'label': '5832.gj.108.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.be1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956762
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.b1', '36.x1.b1', '36.y1.b1', '36.z1.b1', '54.f1.a1'], 'contains': ['216.b1.a1', '324.bc1.b1', '324.bf1.b1', '324.bj1.b1', '324.bk1.b1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3666, -1, 5076, -1, 3096, -1, 4960, -1], 'generators': [3, 288, 4104, 1944], 'label': '5832.gj.108.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.be1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956763
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.a1', '54.g1.a1'], 'contains': ['216.k1.a1', '324.bb1.a1', '324.bl1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5074, -1, 7854, -1, 6576, -1, 7284, -1], 'generators': [39, 2306, 24, 216], 'label': '5832.gj.108.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '108.bf1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956764
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.b1', '54.g1.a1'], 'contains': ['216.k1.a1', '324.bb1.b1', '324.bl1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5074, -1, 7642, -1, 6576, -1, 7241, -1], 'generators': [3, 2306, 24, 216], 'label': '5832.gj.108.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '108.bf1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956765
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.k1.a1', '18.t1.a1', '27.d1.a1', '27.g1.a1', '27.h1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8369, -1, 7966, -1, 7472, -1, 8736, -1], 'generators': [3, 4104, 504, 18, 1944, 36, 24], 'label': '5832.gj.9.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956766
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1.a1', '54.h1.a1'], 'contains': ['216.m1.a1', '324.be1.a1', '324.bn1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4168, -1, 7109, -1, 3643, -1, 6148, -1], 'generators': [39, 2306, 1152, 1944], 'label': '5832.gj.108.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '108.bg1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956767
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1.b1', '54.h1.a1'], 'contains': ['216.m1.a1', '324.be1.b1', '324.bn1.b1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4168, -1, 6535, -1, 3643, -1, 6036, -1], 'generators': [3, 2306, 1152, 1944], 'label': '5832.gj.108.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '108.bg1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956768
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1.a1', '54.i1.a1'], 'contains': ['216.n1.a1', '324.bf1.a1', '324.bm1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4782, -1, 6615, -1, 5047, -1, 6745, -1], 'generators': [39, 4392, 24, 1944], 'label': '5832.gj.108.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.g1.a1', 'old_label': '108.bh1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956769
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1.b1', '54.i1.a1'], 'contains': ['216.n1.a1', '324.bf1.b1', '324.bm1.b1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4782, -1, 6428, -1, 5047, -1, 6527, -1], 'generators': [3, 4392, 24, 1944], 'label': '5832.gj.108.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.g1.a1', 'old_label': '108.bh1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956770
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.a1', '36.s1.a1', '54.j1.a1'], 'contains': ['216.q2.a1', '324.bg1.a1', '324.bp1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [95, -1, 668, -1, 37, -1, 1360, -1], 'generators': [39, 2, 3552, 2160], 'label': '5832.gj.108.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bi1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956771
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.c1', '36.s1.a1', '54.j1.b1'], 'contains': ['216.q2.b1', '324.bg1.a1', '324.bp1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [95, -1, 1114, -1, 37, -1, 1835, -1], 'generators': [39, 2, 1608, 2160], 'label': '5832.gj.108.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '108.bi1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956772
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.b1', '36.s1.a1', '54.j1.c1'], 'contains': ['216.q2.c1', '324.bg1.a1', '324.bp1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [95, -1, 1716, -1, 37, -1, 1499, -1], 'generators': [39, 2, 5496, 2160], 'label': '5832.gj.108.bi1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.bi1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956773
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.d1', '36.s1.b1', '54.j1.a1'], 'contains': ['216.q2.a1', '324.bg1.b1', '324.bp1.d1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [95, -1, 103, -1, 37, -1, 711, -1], 'generators': [3, 2, 3552, 2160], 'label': '5832.gj.108.bi1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bi1.d1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956774
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.f1', '36.s1.b1', '54.j1.b1'], 'contains': ['216.q2.b1', '324.bg1.b1', '324.bp1.e1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [95, -1, 335, -1, 37, -1, 1181, -1], 'generators': [3, 2, 1608, 2160], 'label': '5832.gj.108.bi1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '108.bi1.e1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1.e1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956775
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.e1', '36.s1.b1', '54.j1.c1'], 'contains': ['216.q2.c1', '324.bg1.b1', '324.bp1.f1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [95, -1, 913, -1, 37, -1, 850, -1], 'generators': [3, 2, 5496, 2160], 'label': '5832.gj.108.bi1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.bi1.f1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1.f1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956776
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '9.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.a1'], 'contains': ['18.b1.a1', '18.m1.a1', '18.v1.a1', '27.d1.a1', '27.i1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7245, -1, 7690, -1, 6238, -1, 7686, -1], 'generators': [3, 216, 504, 18, 1944, 36, 3096], 'label': '5832.gj.9.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.e1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956777
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '54.k1.a1'], 'contains': ['216.r1.a1', '324.bh1.a1', '324.bo1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3923, -1, 6186, -1, 4045, -1, 4632, -1], 'generators': [39, 2, 24, 4104], 'label': '5832.gj.108.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1.a1', 'old_label': '108.bj1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956778
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.b1', '54.k1.a1'], 'contains': ['216.r1.a1', '324.bh1.b1', '324.bo1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3923, -1, 6148, -1, 4045, -1, 4448, -1], 'generators': [3, 2, 24, 4104], 'label': '5832.gj.108.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1.a1', 'old_label': '108.bj1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956779
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.a1', '36.s2.a1', '54.l1.a1'], 'contains': ['216.s1.a1', '324.bh1.a1', '324.bp1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [22, -1, 611, -1, 110, -1, 1410, -1], 'generators': [39, 2234, 3552, 2160], 'label': '5832.gj.108.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bk1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956780
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.c1', '36.s2.a1', '54.l1.b1'], 'contains': ['216.s1.b1', '324.bh1.a1', '324.bp1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [22, -1, 1157, -1, 110, -1, 1885, -1], 'generators': [39, 2234, 1608, 2160], 'label': '5832.gj.108.bk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '108.bk1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956781
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.b1', '36.s2.a1', '54.l1.c1'], 'contains': ['216.s1.c1', '324.bh1.a1', '324.bp1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [22, -1, 1776, -1, 110, -1, 1549, -1], 'generators': [39, 2234, 5496, 2160], 'label': '5832.gj.108.bk1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.bk1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956782
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.d1', '36.s2.b1', '54.l1.a1'], 'contains': ['216.s1.a1', '324.bh1.b1', '324.bp1.d1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [22, -1, 406, -1, 110, -1, 761, -1], 'generators': [3, 2234, 3552, 2160], 'label': '5832.gj.108.bk1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bk1.d1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956783
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.f1', '36.s2.b1', '54.l1.b1'], 'contains': ['216.s1.b1', '324.bh1.b1', '324.bp1.e1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [22, -1, 519, -1, 110, -1, 1231, -1], 'generators': [3, 2234, 1608, 2160], 'label': '5832.gj.108.bk1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '108.bk1.e1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1.e1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956784
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.e1', '36.s2.b1', '54.l1.c1'], 'contains': ['216.s1.c1', '324.bh1.b1', '324.bp1.f1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [22, -1, 1070, -1, 110, -1, 900, -1], 'generators': [3, 2234, 5496, 2160], 'label': '5832.gj.108.bk1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.bk1.f1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1.f1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956785
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.a1', '36.v1.a1', '54.m1.a1'], 'contains': ['216.u2.a1', '324.bi1.a1', '324.bp1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [165, -1, 470, -1, 168, -1, 1310, -1], 'generators': [39, 4466, 3552, 2160], 'label': '5832.gj.108.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bl1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956786
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.c1', '36.v1.a1', '54.m1.b1'], 'contains': ['216.u2.b1', '324.bi1.a1', '324.bp1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [165, -1, 818, -1, 168, -1, 1785, -1], 'generators': [39, 4466, 1608, 2160], 'label': '5832.gj.108.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '108.bl1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956787
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.f1.a1', '6.i1.a1'], 'contains': ['24.a1.a1', '36.a1.a1', '36.b1.a1', '36.d1.a1', '36.g1.a1', '36.j1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6898, 9299, 7370, 7582, 5290, 7839, 6940, 8076], 'generators': [36, 1944, 4104, 2, 24, 288], 'label': '5832.gj.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1'], 'normal_contains': ['24.a1.a1', '36.a1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '2916.ef', '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': '324.117'}
  • id: 227956788
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.b1', '36.v1.a1', '54.m1.c1'], 'contains': ['216.u2.c1', '324.bi1.a1', '324.bp1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [165, -1, 1362, -1, 168, -1, 1450, -1], 'generators': [39, 4466, 5496, 2160], 'label': '5832.gj.108.bl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.bl1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956789
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.d1', '36.v1.b1', '54.m1.a1'], 'contains': ['216.u2.a1', '324.bi1.b1', '324.bp1.d1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [165, -1, 14, -1, 168, -1, 661, -1], 'generators': [3, 4466, 3552, 2160], 'label': '5832.gj.108.bl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bl1.d1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956790
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.f1', '36.v1.b1', '54.m1.b1'], 'contains': ['216.u2.b1', '324.bi1.b1', '324.bp1.e1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [165, -1, 184, -1, 168, -1, 1131, -1], 'generators': [3, 4466, 1608, 2160], 'label': '5832.gj.108.bl1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '108.bl1.e1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1.e1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956791
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.e1', '36.v1.b1', '54.m1.c1'], 'contains': ['216.u2.c1', '324.bi1.b1', '324.bp1.f1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [165, -1, 861, -1, 168, -1, 800, -1], 'generators': [3, 4466, 5496, 2160], 'label': '5832.gj.108.bl1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.bl1.f1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1.f1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956792
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.a1', '36.y1.a1', '54.n1.a1'], 'contains': ['216.x1.a1', '324.bj1.a1', '324.bp1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [635, -1, 1299, -1, 225, -1, 1589, -1], 'generators': [39, 2232, 3552, 2160], 'label': '5832.gj.108.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bm1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956793
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.b1', '36.y1.a1', '54.n1.b1'], 'contains': ['216.x1.b1', '324.bj1.a1', '324.bp1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [635, -1, 2073, -1, 225, -1, 1628, -1], 'generators': [39, 2232, 5496, 2160], 'label': '5832.gj.108.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.bm1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956794
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.c1', '36.y1.a1', '54.n1.c1'], 'contains': ['216.x1.c1', '324.bj1.a1', '324.bp1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [635, -1, 1584, -1, 225, -1, 1924, -1], 'generators': [39, 2232, 1608, 2160], 'label': '5832.gj.108.bm1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '108.bm1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956795
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.d1', '36.y1.b1', '54.n1.a1'], 'contains': ['216.x1.a1', '324.bj1.b1', '324.bp1.d1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [635, -1, 1191, -1, 225, -1, 940, -1], 'generators': [3, 2232, 3552, 2160], 'label': '5832.gj.108.bm1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bm1.d1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956796
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.e1', '36.y1.b1', '54.n1.b1'], 'contains': ['216.x1.b1', '324.bj1.b1', '324.bp1.f1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [635, -1, 1982, -1, 225, -1, 979, -1], 'generators': [3, 2232, 5496, 2160], 'label': '5832.gj.108.bm1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '108.bm1.e1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1.e1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956797
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.f1', '36.y1.b1', '54.n1.c1'], 'contains': ['216.x1.c1', '324.bj1.b1', '324.bp1.e1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [635, -1, 1511, -1, 225, -1, 1271, -1], 'generators': [3, 2232, 1608, 2160], 'label': '5832.gj.108.bm1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '108.bm1.f1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1.f1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956798
    {'ambient': '5832.gj', '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': '972.a1.a1', 'complements': ['2916.b1.b1', '2916.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.a1', '6.d1.a1', '6.i1.a1', '6.l1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7814, 4442, 8220, 5485, 6601, 5434, 7556, 5082], 'generators': [18, 3096, 4392, 2, 36, 1944, 216, 24], 'label': '5832.gj.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.c1.a1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '2916.ef', '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': '972.446'}
  • id: 227956799
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.c1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.b1.a1', '36.a1.a1', '36.c1.a1', '36.f1.a1', '36.i1.a1', '36.m1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6084, 5558, 6863, 3741, 4398, 6361, 6764, 5684], 'generators': [36, 1944, 4104, 2, 1152, 288], 'label': '5832.gj.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.c1.a1'], 'normal_contains': ['24.b1.a1', '36.a1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '2916.ef', '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': '324.117'}
  • id: 227956800
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '36.u1.a1', '36.x1.a1', '54.o1.a1'], 'contains': ['216.d1.a1', '324.bk1.a1', '324.bl1.a1', '324.bm1.a1', '324.bo1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4601, -1, 6497, -1, 5114, -1, 6481, -1], 'generators': [39, 24, 216, 1944], 'label': '5832.gj.108.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.bn1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956801
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.b1', '36.u1.b1', '36.x1.b1', '54.o1.a1'], 'contains': ['216.d1.a1', '324.bk1.b1', '324.bl1.b1', '324.bm1.b1', '324.bo1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4601, -1, 5995, -1, 5114, -1, 6432, -1], 'generators': [3, 24, 216, 1944], 'label': '5832.gj.108.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.bn1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956802
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1.a1', '36.s2.a1', '36.v1.a1', '36.y1.a1', '54.p1.a1'], 'contains': ['216.f1.a1', '324.bk1.a1', '324.bp1.a1', '324.bp1.b1', '324.bp1.c1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2028, -1, 1672, -1, 1385, -1, 1668, -1], 'generators': [39, 3768, 1944, 2160], 'label': '5832.gj.108.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.bo1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956803
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1.b1', '36.s2.b1', '36.v1.b1', '36.y1.b1', '54.p1.a1'], 'contains': ['216.f1.a1', '324.bk1.b1', '324.bp1.d1', '324.bp1.e1', '324.bp1.f1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2028, -1, 771, -1, 1385, -1, 1019, -1], 'generators': [3, 3768, 1944, 2160], 'label': '5832.gj.108.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '108.bo1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956804
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '36.w1.a1', '36.z1.a1', '54.q1.a1'], 'contains': ['216.h1.a1', '324.bk1.a1', '324.bn1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3865, -1, 5529, -1, 3375, -1, 5961, -1], 'generators': [39, 3096, 216, 1944], 'label': '5832.gj.108.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.bp1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956805
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.b1', '36.w1.b1', '36.z1.b1', '54.q1.a1'], 'contains': ['216.h1.a1', '324.bk1.b1', '324.bn1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3865, -1, 5344, -1, 3375, -1, 5823, -1], 'generators': [3, 3096, 216, 1944], 'label': '5832.gj.108.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.bp1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956806
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '81.a1.a1'], 'contains': ['324.x1.a1', '324.z1.a1', '324.z1.b1', '486.a1.a1', '486.b1.a1', '486.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5099, -1, 7946, -1, 5954, -1, 5998, -1], 'generators': [3, 36, 2, 4392], 'label': '5832.gj.162.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956807
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.d1.a1'], 'contains': ['324.b1.a1', '324.ba1.a1', '324.ba1.b1', '486.a1.a1', '486.d1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3652, -1, 6710, -1, 4973, -1, 5653, -1], 'generators': [3, 36, 2, 216], 'label': '5832.gj.162.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956808
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.e1.a1', '54.g1.a1', '81.b1.a1'], 'contains': ['324.c1.a1', '324.bb1.a1', '324.bb1.b1', '486.b1.a1', '486.d1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6369, -1, 8958, -1, 6651, -1, 6796, -1], 'generators': [3, 36, 2306, 216], 'label': '5832.gj.162.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956809
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.f1.a1', '81.c1.a1'], 'contains': ['324.d1.a1', '324.bc1.a1', '324.bc1.b1', '486.c1.a1', '486.d1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6742, -1, 8080, -1, 6206, -1, 6694, -1], 'generators': [3, 36, 4392, 216], 'label': '5832.gj.162.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956810
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.c1.a1', '36.b1.a1', '36.c1.a1', '36.k1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5961, 3746, 6579, 5359, 3884, 3556, 6473, 4264], 'generators': [36, 1944, 216, 24, 1152, 288], 'label': '5832.gj.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.e1.a1', '6.d1.a1'], 'normal_contains': ['24.c1.a1', '36.b1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
  • id: 227956811
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '54.d1.a1'], 'contains': ['324.g1.a1', '324.bd1.a1', '324.bd1.b1', '486.a1.a1', '486.e1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3803, -1, 6919, -1, 4565, -1, 5594, -1], 'generators': [3, 36, 2, 1944], 'label': '5832.gj.162.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '162.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956812
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '54.e1.a1', '54.h1.a1', '81.d1.a1'], 'contains': ['324.h1.a1', '324.be1.a1', '324.be1.b1', '486.b1.a1', '486.e1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5833, -1, 7394, -1, 5885, -1, 6578, -1], 'generators': [3, 36, 2306, 1944], 'label': '5832.gj.162.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '162.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956813
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '54.f1.a1', '54.i1.a1', '81.e1.a1'], 'contains': ['324.i1.a1', '324.bf1.a1', '324.bf1.b1', '486.c1.a1', '486.e1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6567, -1, 8015, -1, 6022, -1, 6636, -1], 'generators': [3, 36, 4392, 1944], 'label': '5832.gj.162.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '162.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956814
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '54.d1.a1', '54.j1.a1', '54.j1.b1', '54.j1.c1'], 'contains': ['324.n1.a1', '324.bg1.a1', '324.bg1.b1', '486.a1.a1', '486.f1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2612, -1, 314, -1, 2278, -1, 4141, -1], 'generators': [3, 36, 2, 2160], 'label': '5832.gj.162.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '162.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956815
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '54.d1.a1', '54.k1.a1', '54.l1.a1', '54.l1.b1', '54.l1.c1'], 'contains': ['324.o1.a1', '324.bh1.a1', '324.bh1.b1', '486.a1.a1', '486.f1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2240, -1, 756, -1, 2638, -1, 4199, -1], 'generators': [3, 36, 2, 4104], 'label': '5832.gj.162.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '162.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956816
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '54.e1.a1', '54.m1.a1', '54.m1.b1', '54.m1.c1'], 'contains': ['324.p1.a1', '324.bi1.a1', '324.bi1.b1', '486.b1.a1', '486.f1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2530, -1, 172, -1, 2363, -1, 4083, -1], 'generators': [3, 36, 2306, 4104], 'label': '5832.gj.162.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '162.j1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956817
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '54.f1.a1', '54.n1.a1', '54.n1.b1', '54.n1.c1'], 'contains': ['324.r1.a1', '324.bj1.a1', '324.bj1.b1', '486.c1.a1', '486.f1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2763, -1, 1712, -1, 2448, -1, 4257, -1], 'generators': [3, 36, 4392, 4104], 'label': '5832.gj.162.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '162.k1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956818
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '54.e1.a1', '54.f1.a1', '54.o1.a1', '54.p1.a1', '54.q1.a1', '81.f1.a1'], 'contains': ['324.a1.a1', '324.bk1.a1', '324.bk1.b1', '486.d1.a1', '486.e1.a1', '486.f1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6209, -1, 6097, -1, 4470, -1, 6371, -1], 'generators': [3, 36, 216, 1944], 'label': '5832.gj.162.l1.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': '162.l1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.l1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956819
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.g1.a1', '54.o1.a1', '81.g1.a1'], 'contains': ['324.e1.a1', '324.bl1.a1', '324.bl1.b1', '486.d1.a1', '486.g1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7027, -1, 9442, -1, 7261, -1, 8002, -1], 'generators': [3, 36, 24, 216], 'label': '5832.gj.162.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '162.m1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.m1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956820
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.i1.a1', '54.o1.a1', '81.h1.a1'], 'contains': ['324.j1.a1', '324.bm1.a1', '324.bm1.b1', '486.e1.a1', '486.g1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6926, -1, 7766, -1, 6988, -1, 7930, -1], 'generators': [3, 36, 24, 1944], 'label': '5832.gj.162.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.g1.a1', 'old_label': '162.n1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.n1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956821
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': ['486.l1.a1', '486.r1.a1', '486.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '36.x1.a1', '36.y1.a1', '36.z1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3843, 1111, 5354, 2418, 3292, 1081, 5509, 1060], 'generators': [39, 1944, 216, 24, 3096, 288], 'label': '5832.gj.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2916.ef'}
  • id: 227956822
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.h1.a1', '54.q1.a1', '81.i1.a1'], 'contains': ['324.l1.a1', '324.bn1.a1', '324.bn1.b1', '486.e1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5994, -1, 7267, -1, 5605, -1, 6845, -1], 'generators': [3, 36, 1152, 1944], 'label': '5832.gj.162.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '162.o1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.o1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956823
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.k1.a1', '54.o1.a1'], 'contains': ['324.s1.a1', '324.bo1.a1', '324.bo1.b1', '486.f1.a1', '486.g1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4148, -1, 7161, -1, 5305, -1, 5718, -1], 'generators': [3, 36, 24, 4104], 'label': '5832.gj.162.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1.a1', 'old_label': '162.p1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.p1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956824
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.a1', '54.l1.a1', '54.m1.a1', '54.n1.a1', '54.p1.a1'], 'contains': ['324.u1.a1', '324.bp1.a1', '324.bp1.d1', '486.f1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [767, -1, 228, -1, 388, -1, 1707, -1], 'generators': [3, 36, 3552, 2160], 'label': '5832.gj.162.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '162.q1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.q1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956825
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.b1', '54.l1.b1', '54.m1.b1', '54.n1.c1', '54.p1.a1'], 'contains': ['324.u1.b1', '324.bp1.b1', '324.bp1.e1', '486.f1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [767, -1, 471, -1, 388, -1, 1964, -1], 'generators': [3, 36, 1608, 2160], 'label': '5832.gj.162.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '162.q1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.q1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956826
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.c1', '54.l1.c1', '54.m1.c1', '54.n1.b1', '54.p1.a1'], 'contains': ['324.u1.c1', '324.bp1.c1', '324.bp1.f1', '486.f1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [767, -1, 1384, -1, 388, -1, 1746, -1], 'generators': [3, 36, 5496, 2160], 'label': '5832.gj.162.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '162.q1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.q1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956827
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.r1.a1', '54.t1.a1', '54.v1.a1', '54.x1.a1', '54.y1.a1', '81.f1.a1'], 'contains': ['324.a1.a1', '486.h1.a1', '486.j1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9085, -1, 8811, -1, 8864, -1, 9373, -1], 'generators': [18, 216, 36, 1944], 'label': '5832.gj.162.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.r1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956828
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.s1.a1', '54.u1.a1', '54.w1.a1', '54.z1.a1', '54.ba1.a1', '81.f1.a1'], 'contains': ['324.a1.a1', '486.i1.a1', '486.k1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8677, -1, 7856, -1, 7366, -1, 9252, -1], 'generators': [21, 1944, 36, 216], 'label': '5832.gj.162.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '162.s1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956829
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.t1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.r1.a1', '54.bb1.a1', '54.bd1.a1', '81.b1.a1'], 'contains': ['324.c1.a1', '486.h1.a1', '486.l1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8168, -1, 9638, -1, 9560, -1, 8762, -1], 'generators': [18, 2522, 216, 36], 'label': '5832.gj.162.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '162.t1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956830
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.s1.a1', '54.bc1.a1', '54.be1.a1', '54.be2.a1', '81.b1.a1'], 'contains': ['324.c1.a1', '486.i1.a1', '486.m1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7921, -1, 9351, -1, 8481, -1, 9445, -1], 'generators': [21, 578, 36, 216], 'label': '5832.gj.162.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '162.u1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956831
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.t1.a1', '54.bb1.a1', '81.c1.a1'], 'contains': ['324.d1.a1', '486.h1.a1', '486.n1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8823, -1, 9029, -1, 9280, -1, 8691, -1], 'generators': [18, 216, 36, 504], 'label': '5832.gj.162.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.v1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.v1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956832
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': ['486.l1.a1', '486.r1.a1', '486.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.a1'], 'contains': ['24.c1.a1', '36.x1.b1', '36.y1.b1', '36.z1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3843, 1111, 4871, 968, 3292, 1081, 5389, 2060], 'generators': [3, 1944, 216, 24, 3096, 288], 'label': '5832.gj.12.d1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.a1'], 'normal_contains': ['24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.b1', 'projective_image': '5832.gj', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': '2916.ef'}
  • id: 227956833
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.u1.a1', '54.bc1.a1', '81.c1.a1'], 'contains': ['324.d1.a1', '486.i1.a1', '486.o1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8490, -1, 8759, -1, 7871, -1, 9312, -1], 'generators': [21, 36, 4392, 216], 'label': '5832.gj.162.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '162.w1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.w1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956834
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.v1.a1', '54.bd1.a1', '81.g1.a1'], 'contains': ['324.e1.a1', '486.h1.a1', '486.p1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9880, -1, 9762, -1, 9852, -1, 9862, -1], 'generators': [18, 24, 216, 36], 'label': '5832.gj.162.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '162.x1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.x1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956835
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.w1.a1', '54.be1.a1', '54.be2.a1', '81.g1.a1'], 'contains': ['324.e1.a1', '486.i1.a1', '486.q1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9750, -1, 9814, -1, 9473, -1, 9979, -1], 'generators': [21, 36, 24, 216], 'label': '5832.gj.162.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.y1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.y1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956836
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.x1.a1', '54.bd1.a1'], 'contains': ['324.f1.a1', '486.h1.a1', '486.r1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9978, -1, 9986, -1, 9955, -1, 9791, -1], 'generators': [18, 4490, 216, 36], 'label': '5832.gj.162.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bd1.a1', 'old_label': '162.z1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.z1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956837
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.r1.a1', '54.bf1.a1', '54.bh1.a1', '54.bh2.a1', '81.d1.a1'], 'contains': ['324.h1.a1', '486.j1.a1', '486.l1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7797, -1, 9183, -1, 8044, -1, 8261, -1], 'generators': [18, 578, 36, 1944], 'label': '5832.gj.162.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '162.ba1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956838
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bb1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.s1.a1', '54.bg1.a1', '54.bi1.a1', '81.d1.a1'], 'contains': ['324.h1.a1', '486.k1.a1', '486.m1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7573, -1, 8887, -1, 7469, -1, 8405, -1], 'generators': [21, 2306, 1944, 36], 'label': '5832.gj.162.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '162.bb1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956839
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.t1.a1', '54.bf1.a1', '54.bj1.a1', '54.bl1.a1', '81.e1.a1'], 'contains': ['324.i1.a1', '486.j1.a1', '486.n1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8977, -1, 8544, -1, 8776, -1, 8822, -1], 'generators': [18, 36, 4392, 1944], 'label': '5832.gj.162.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '162.bc1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956840
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.u1.a1', '54.bg1.a1', '54.bk1.a1', '81.e1.a1'], 'contains': ['324.i1.a1', '486.k1.a1', '486.o1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8576, -1, 7689, -1, 7574, -1, 8954, -1], 'generators': [21, 1944, 36, 4176], 'label': '5832.gj.162.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '162.bd1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956841
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.v1.a1', '54.bj1.a1', '81.h1.a1'], 'contains': ['324.j1.a1', '486.j1.a1', '486.p1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9402, -1, 8421, -1, 9385, -1, 9648, -1], 'generators': [18, 24, 36, 1944], 'label': '5832.gj.162.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.h1.a1', 'old_label': '162.be1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.be1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956842
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.w1.a1', '54.bk1.a1', '81.h1.a1'], 'contains': ['324.j1.a1', '486.k1.a1', '486.q1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9278, -1, 8209, -1, 8376, -1, 9720, -1], 'generators': [21, 1944, 36, 24], 'label': '5832.gj.162.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.h1.a1', 'old_label': '162.bf1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956843
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.g1.a1'], 'contains': ['24.d1.a1', '36.a1.a1', '36.e1.a1', '36.e2.a1', '36.h1.a1', '36.k1.a1', '36.l1.a1', '36.n1.a1', '36.n1.b1', '36.n1.c1', '36.o1.a1', '36.o1.b1', '36.o1.c1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2149, -1, 4289, -1, 2102, -1, 3089, -1], 'generators': [36, 2160, 1944, 2, 1464, 288], 'label': '5832.gj.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 227956844
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.x1.a1', '54.bl1.a1'], 'contains': ['324.k1.a1', '486.j1.a1', '486.r1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9503, -1, 9924, -1, 9664, -1, 9575, -1], 'generators': [18, 2546, 36, 1944], 'label': '5832.gj.162.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1.a1', 'old_label': '162.bg1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956845
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.y1.a1', '54.bh1.a1', '54.bh2.a1', '81.i1.a1'], 'contains': ['324.l1.a1', '486.j1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7227, -1, 8315, -1, 7180, -1, 8057, -1], 'generators': [18, 36, 1152, 1944], 'label': '5832.gj.162.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '162.bh1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956846
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.z1.a1', '54.bi1.a1', '81.i1.a1'], 'contains': ['324.l1.a1', '486.k1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7104, -1, 7465, -1, 7123, -1, 8096, -1], 'generators': [21, 5040, 36, 1944], 'label': '5832.gj.162.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '162.bi1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956847
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bj1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.ba1.a1', '54.bi1.a1'], 'contains': ['324.m1.a1', '486.k1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7281, -1, 7598, -1, 7068, -1, 8134, -1], 'generators': [21, 650, 36, 1944], 'label': '5832.gj.162.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bi1.a1', 'old_label': '162.bj1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956848
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bb1.a1', '54.bf1.a1', '81.a1.a1'], 'contains': ['324.x1.a1', '486.l1.a1', '486.n1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8045, -1, 9504, -1, 8688, -1, 8333, -1], 'generators': [18, 2, 36, 4392], 'label': '5832.gj.162.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.bk1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956849
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bc1.a1', '54.bg1.a1', '81.a1.a1'], 'contains': ['324.x1.a1', '486.m1.a1', '486.o1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7673, -1, 9245, -1, 7784, -1, 8546, -1], 'generators': [21, 2, 36, 4392], 'label': '5832.gj.162.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '162.bl1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956850
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bb1.a1', '54.bf1.a1'], 'contains': ['324.y1.a1', '486.l1.a1', '486.n1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8268, -1, 9700, -1, 9090, -1, 8189, -1], 'generators': [18, 218, 36, 4392], 'label': '5832.gj.162.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bb1.a1', 'old_label': '162.bm1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956851
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '162.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bc1.a1', '54.bg1.a1'], 'contains': ['324.y2.a1', '486.m1.a1', '486.o1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7428, -1, 9092, -1, 7679, -1, 8619, -1], 'generators': [21, 218, 36, 3960], 'label': '5832.gj.162.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.bg1.a1', 'old_label': '162.bn1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956852
    {'ambient': '5832.gj', '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': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.g1.a1', '72.h1.a1', '72.i1.a1', '108.a1.a1', '108.bd1.a1', '108.bd1.b1'], 'contains': ['648.a1.a1', '648.c1.a1', '648.h1.a1', '648.p1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4464, 5736, 5672, 4402, 3647, 6173, 5391, 6188], 'generators': [578, 216, 1944], 'label': '5832.gj.216.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.a1.a1', '108.a1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '36.10', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956853
    {'ambient': '5832.gj', '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': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '72.m1.a1', '108.b1.a1', '108.be1.a1', '108.be1.b1'], 'contains': ['648.a1.a1', '648.d1.a1', '648.i1.a1', '648.r1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4514, 5005, 5214, 3749, 3281, 5528, 5218, 5614], 'generators': [288, 216, 1944], 'label': '5832.gj.216.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '108.b1.a1'], 'normal_contains': ['648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '36.10', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956854
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.k1.a1'], 'contains': ['24.e1.a1', '36.b1.a1', '36.l1.a1', '36.m1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6409, -1, 6743, -1, 3747, -1, 6852, -1], 'generators': [36, 1944, 216, 1154, 24, 2016], 'label': '5832.gj.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '12.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
  • id: 227956855
    {'ambient': '5832.gj', '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': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.d1.a1', '72.e1.a1', '72.e2.a1', '72.f1.a1', '108.c1.a1', '108.bc1.a1', '108.bc1.b1'], 'contains': ['648.a1.a1', '648.b1.a1', '648.g1.a1', '648.n1.a1', '648.o1.a1', '648.q1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1554, -1, 5074, -1, 3144, -1, 4553, -1], 'generators': [2, 216, 1944], 'label': '5832.gj.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '5832.gj', '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': '6.1'}
  • id: 227956856
    {'ambient': '5832.gj', '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': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.d1.a1', '72.g1.a1', '108.d1.a1', '108.bn1.a1', '108.bn1.b1'], 'contains': ['648.a1.a1', '648.e1.a1', '648.j1.a1', '648.s1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5669, -1, 6022, -1, 5062, -1, 6541, -1], 'generators': [24, 216, 1944], 'label': '5832.gj.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.d1.a1', 'projective_image': '5832.gj', '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': '36.12'}
  • id: 227956857
    {'ambient': '5832.gj', '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': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.g1.a1', '72.j1.a1', '108.e1.a1'], 'contains': ['648.a1.a1', '648.f1.a1', '648.k1.a1', '648.t1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5786, -1, 6139, -1, 4651, -1, 6506, -1], 'generators': [26, 216, 1944], 'label': '5832.gj.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '216.e1.a1', 'projective_image': '5832.gj', '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': '18.3'}
  • id: 227956858
    {'ambient': '5832.gj', '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': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.e2.a1', '72.h1.a1', '72.k1.a1', '108.f1.a1', '108.bo1.a1', '108.bo1.b1'], 'contains': ['648.a1.a1', '648.u1.a1', '648.u1.b1', '648.u1.c1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1877, -1, 2208, -1, 1574, -1, 1201, -1], 'generators': [1464, 1944], 'label': '5832.gj.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.f1.a1', 'projective_image': '5832.gj', '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': '6.2'}
  • id: 227956859
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.e2.a1', '72.h1.a1', '72.l1.a1', '108.g1.a1'], 'contains': ['648.a1.a1', '648.v1.a1', '648.v1.b1', '648.v1.c1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2170, -1, 2840, -1, 1670, -1, 904, -1], 'generators': [1178, 1944], 'label': '5832.gj.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.g1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956860
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.f1.a1', '72.i1.a1', '108.h1.a1', '108.bp1.a1', '108.bp1.b1'], 'contains': ['648.a1.a1', '648.l1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4672, -1, 5402, -1, 3578, -1, 6122, -1], 'generators': [1152, 216], 'label': '5832.gj.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '216.h1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 227956861
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.i1.a1', '72.m1.a1', '108.i1.a1'], 'contains': ['648.a1.a1', '648.m1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4948, -1, 4969, -1, 3493, -1, 6211, -1], 'generators': [1154, 216], 'label': '5832.gj.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '216.i1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956862
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '108.j1.a1', '108.z1.a1', '108.z1.b1'], 'contains': ['648.b1.a1', '648.c1.a1', '648.d1.a1', '648.w1.a1', '648.x1.a1', '648.y1.a1', '648.y2.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3412, -1, 6311, -1, 4110, -1, 4908, -1], 'generators': [2, 288, 216], 'label': '5832.gj.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.j1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 227956863
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '108.k1.a1', '108.bf1.a1', '108.bf1.b1'], 'contains': ['648.c1.a1', '648.e1.a1', '648.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9113, -1, 7833, -1, 6544, -1, 7346, -1], 'generators': [2306, 24], 'label': '5832.gj.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '216.k1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956864
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '108.k2.a1'], 'contains': ['648.c1.a1', '648.e1.a1', '648.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9060, -1, 7777, -1, 6499, -1, 7377, -1], 'generators': [362, 24], 'label': '5832.gj.216.k2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.q1.a1', 'old_label': '216.k2.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k2.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956865
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['24.f1.a1', '36.j1.a1', '36.k1.a1', '36.l1.a1', '36.m1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3271, -1, 6662, -1, 3175, -1, 5587, -1], 'generators': [36, 1944, 216, 1154, 1464, 72], 'label': '5832.gj.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 227956866
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '108.l1.a1', '108.ba1.a1', '108.ba1.b1'], 'contains': ['648.g1.a1', '648.h1.a1', '648.i1.a1', '648.w1.a1', '648.x1.a1', '648.y1.a1', '648.y2.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3135, -1, 6540, -1, 3784, -1, 4873, -1], 'generators': [2, 288, 1944], 'label': '5832.gj.216.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.l1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 227956867
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '108.m1.a1', '108.bg1.a1', '108.bg1.b1'], 'contains': ['648.h1.a1', '648.l1.a1', '648.m1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4879, -1, 6742, -1, 3839, -1, 6468, -1], 'generators': [2306, 5040], 'label': '5832.gj.216.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '216.m1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956868
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.m2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '108.m2.a1'], 'contains': ['648.h1.a1', '648.l1.a1', '648.m1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5179, -1, 6644, -1, 4340, -1, 6579, -1], 'generators': [2522, 5040], 'label': '5832.gj.216.m2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.r1.a1', 'old_label': '216.m2.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m2.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956869
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '108.n1.a1', '108.bh1.a1', '108.bh1.b1'], 'contains': ['648.i1.a1', '648.j1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5739, -1, 6411, -1, 4785, -1, 6704, -1], 'generators': [24, 288], 'label': '5832.gj.216.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '216.n1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956870
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '108.o1.a1'], 'contains': ['648.i1.a1', '648.k1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6590, -1, 6845, -1, 5453, -1, 6614, -1], 'generators': [26, 4176], 'label': '5832.gj.216.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1.a1', 'old_label': '216.o1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956871
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.n1.a1', '72.n1.b1', '72.n1.c1', '108.p1.a1'], 'contains': ['648.n1.a1', '648.p1.a1', '648.q1.a1', '648.r1.a1', '648.w1.a1', '648.y1.a1', '648.y2.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1989, -1, 3987, -1, 2791, -1, 2124, -1], 'generators': [1946, 288, 4104], 'label': '5832.gj.216.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.p1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956872
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.n1.a1', '72.n1.b1', '72.o1.b1', '108.q1.a1'], 'contains': ['648.n1.a1', '648.u1.a1', '648.v1.b1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [428, -1, 3022, -1, 908, -1, 550, -1], 'generators': [2, 5784], 'label': '5832.gj.216.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.q1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956873
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.n1.a1', '72.n1.c1', '72.o1.a1', '108.q1.b1'], 'contains': ['648.n1.a1', '648.u1.b1', '648.v1.a1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [428, -1, 3185, -1, 908, -1, 292, -1], 'generators': [2, 3840], 'label': '5832.gj.216.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.q1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956874
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.n1.b1', '72.n1.c1', '72.o1.c1', '108.q1.c1'], 'contains': ['648.n1.a1', '648.u1.c1', '648.v1.a1', '648.v1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [428, -1, 3279, -1, 908, -1, 609, -1], 'generators': [2, 1896], 'label': '5832.gj.216.q1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.q1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956875
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.q2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.n1.b1', '72.o1.a1', '108.q2.a1', '108.bi1.a1', '108.bi1.d1'], 'contains': ['648.n1.a1', '648.u1.a1', '648.v1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [267, -1, 1469, -1, 610, -1, 667, -1], 'generators': [1946, 5784], 'label': '5832.gj.216.q2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.q2.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q2.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956876
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.l1.a1'], 'contains': ['24.g1.a1', '36.c1.a1', '36.j1.a1', '36.l1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6253, -1, 6940, -1, 4021, -1, 6567, -1], 'generators': [36, 1944, 216, 26, 1152, 4392], 'label': '5832.gj.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
  • id: 227956877
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.q2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.n1.a1', '72.o1.c1', '108.q2.b1', '108.bi1.b1', '108.bi1.e1'], 'contains': ['648.n1.a1', '648.u1.b1', '648.v1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [267, -1, 2157, -1, 610, -1, 1300, -1], 'generators': [1946, 3840], 'label': '5832.gj.216.q2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.q2.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q2.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956878
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.q2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.n1.c1', '72.o1.b1', '108.q2.c1', '108.bi1.c1', '108.bi1.f1'], 'contains': ['648.n1.a1', '648.u1.c1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [267, -1, 2294, -1, 610, -1, 806, -1], 'generators': [1946, 1896], 'label': '5832.gj.216.q2.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.q2.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q2.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956879
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '108.r1.a1', '108.bj1.a1', '108.bj1.b1'], 'contains': ['648.o1.a1', '648.s1.a1', '648.t1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3973, -1, 5979, -1, 4158, -1, 4632, -1], 'generators': [2, 24], 'label': '5832.gj.216.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '216.r1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956880
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e2.a1', '72.o1.a1', '72.o1.b1', '108.s1.a1', '108.bk1.a1', '108.bk1.d1'], 'contains': ['648.o1.a1', '648.u1.a1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [151, -1, 1169, -1, 721, -1, 717, -1], 'generators': [2234, 5784], 'label': '5832.gj.216.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.s1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956881
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e2.a1', '72.o1.a1', '72.o1.c1', '108.s1.b1', '108.bk1.b1', '108.bk1.e1'], 'contains': ['648.o1.a1', '648.u1.b1', '648.v1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [151, -1, 1540, -1, 721, -1, 1349, -1], 'generators': [2234, 3840], 'label': '5832.gj.216.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.s1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956882
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e2.a1', '72.o1.b1', '72.o1.c1', '108.s1.c1', '108.bk1.c1', '108.bk1.f1'], 'contains': ['648.o1.a1', '648.u1.c1', '648.v1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [151, -1, 2035, -1, 721, -1, 1073, -1], 'generators': [2234, 1896], 'label': '5832.gj.216.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.s1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956883
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.o1.a1', '72.o1.b1', '72.o1.c1', '108.t1.a1', '108.bb1.a1', '108.bb1.b1'], 'contains': ['648.n1.a1', '648.o1.a1', '648.p1.a1', '648.r1.a1', '648.w1.a1', '648.x1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1650, -1, 1896, -1, 2484, -1, 2089, -1], 'generators': [2, 288, 4104], 'label': '5832.gj.216.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.t1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956884
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '72.n1.a1', '72.n1.b1', '72.o1.b1', '108.u1.a1'], 'contains': ['648.p1.a1', '648.u1.a1', '648.v1.b1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [624, -1, 2911, -1, 980, -1, 461, -1], 'generators': [578, 5784], 'label': '5832.gj.216.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.u1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956885
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '72.n1.a1', '72.n1.c1', '72.o1.a1', '108.u1.b1'], 'contains': ['648.p1.a1', '648.u1.b1', '648.v1.a1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [624, -1, 3114, -1, 980, -1, 243, -1], 'generators': [578, 3840], 'label': '5832.gj.216.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.u1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956886
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '72.n1.b1', '72.n1.c1', '72.o1.c1', '108.u1.c1'], 'contains': ['648.p1.a1', '648.u1.c1', '648.v1.a1', '648.v1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [624, -1, 3322, -1, 980, -1, 421, -1], 'generators': [578, 1896], 'label': '5832.gj.216.u1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.u1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956887
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '36.p1.a1', '36.r1.a1', '36.u1.a1', '36.x1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4304, -1, 5998, -1, 4276, -1, 6212, -1], 'generators': [39, 1944, 4104, 2, 288, 24], 'label': '5832.gj.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.i1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956888
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '72.n1.b1', '72.o1.a1', '108.u2.a1', '108.bl1.a1', '108.bl1.d1'], 'contains': ['648.p1.a1', '648.u1.a1', '648.v1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [359, -1, 1308, -1, 779, -1, 501, -1], 'generators': [2522, 5784], 'label': '5832.gj.216.u2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.u2.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u2.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956889
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '72.n1.a1', '72.o1.c1', '108.u2.b1', '108.bl1.b1', '108.bl1.e1'], 'contains': ['648.p1.a1', '648.u1.b1', '648.v1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [359, -1, 1864, -1, 779, -1, 1251, -1], 'generators': [2522, 3840], 'label': '5832.gj.216.u2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.u2.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u2.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956890
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.u2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '72.n1.c1', '72.o1.b1', '108.u2.c1', '108.bl1.c1', '108.bl1.f1'], 'contains': ['648.p1.a1', '648.u1.c1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [359, -1, 2251, -1, 779, -1, 756, -1], 'generators': [2522, 1896], 'label': '5832.gj.216.u2.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.u2.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u2.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956891
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '108.v1.a1'], 'contains': ['648.q1.a1', '648.s1.a1', '648.t1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4279, -1, 6210, -1, 4203, -1, 4663, -1], 'generators': [1946, 24], 'label': '5832.gj.216.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '216.v1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956892
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e2.a1', '72.n1.a1', '72.n1.b1', '108.w1.a1'], 'contains': ['648.q1.a1', '648.u1.a1', '648.v1.a1', '648.v1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [680, -1, 3386, -1, 1254, -1, 993, -1], 'generators': [290, 5784], 'label': '5832.gj.216.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.w1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956893
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e2.a1', '72.n1.a1', '72.n1.c1', '108.w1.b1'], 'contains': ['648.q1.a1', '648.u1.b1', '648.v1.b1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [680, -1, 3438, -1, 1254, -1, 953, -1], 'generators': [290, 3840], 'label': '5832.gj.216.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.w1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956894
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e2.a1', '72.n1.b1', '72.n1.c1', '108.w1.c1'], 'contains': ['648.q1.a1', '648.u1.c1', '648.v1.a1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [680, -1, 3667, -1, 1254, -1, 381, -1], 'generators': [290, 1896], 'label': '5832.gj.216.w1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.w1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956895
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '72.n1.a1', '72.o1.a1', '108.x1.a1', '108.bm1.a1', '108.bm1.d1'], 'contains': ['648.r1.a1', '648.u1.a1', '648.u1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [736, -1, 1751, -1, 836, -1, 1112, -1], 'generators': [1464, 288], 'label': '5832.gj.216.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.x1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956896
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '72.n1.b1', '72.o1.b1', '108.x1.b1', '108.bm1.b1', '108.bm1.e1'], 'contains': ['648.r1.a1', '648.u1.a1', '648.u1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [736, -1, 2336, -1, 836, -1, 1152, -1], 'generators': [3408, 288], 'label': '5832.gj.216.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.x1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1.b1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956897
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '72.n1.c1', '72.o1.c1', '108.x1.c1', '108.bm1.c1', '108.bm1.f1'], 'contains': ['648.r1.a1', '648.u1.b1', '648.u1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [736, -1, 1987, -1, 836, -1, 1451, -1], 'generators': [5352, 288], 'label': '5832.gj.216.x1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '216.x1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227956898
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.f1.a1'], 'contains': ['24.a1.a1', '36.p1.b1', '36.r1.b1', '36.u1.b1', '36.x1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4304, -1, 5875, -1, 4276, -1, 6011, -1], 'generators': [3, 1944, 4104, 2, 288, 24], 'label': '5832.gj.12.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.i1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227956899
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1.a1', '72.n1.a1', '72.n1.b1', '72.o1.c1', '108.y1.a1'], 'contains': ['648.r1.a1', '648.v1.a1', '648.v1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1019, -1, 3703, -1, 1038, -1, 1033, -1], 'generators': [3122, 288], 'label': '5832.gj.216.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.y1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956900
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1.a1', '72.n1.b1', '72.n1.c1', '72.o1.a1', '108.y1.b1'], 'contains': ['648.r1.a1', '648.v1.a1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1019, -1, 3805, -1, 1038, -1, 342, -1], 'generators': [1178, 288], 'label': '5832.gj.216.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.y1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956901
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1.a1', '72.n1.a1', '72.n1.c1', '72.o1.b1', '108.y1.c1'], 'contains': ['648.r1.a1', '648.v1.b1', '648.v1.c1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1019, -1, 3757, -1, 1038, -1, 855, -1], 'generators': [5066, 288], 'label': '5832.gj.216.y1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '216.y1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1.c1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 227956902
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1.a1', '81.b1.a1', '81.d1.a1'], 'contains': ['486.b1.a1', '486.l1.a1', '486.m1.a1', '729.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [7767, -1, 9332, -1, 8584, -1, 8475, -1], 'generators': [3, 18, 2306, 36], 'label': '5832.gj.243.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1.a1', 'old_label': '243.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227956903
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '243.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1.a1', '81.c1.a1', '81.e1.a1'], 'contains': ['486.c1.a1', '486.n1.a1', '486.o1.a1', '729.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8154, -1, 8860, -1, 8271, -1, 8882, -1], 'generators': [3, 18, 36, 4392], 'label': '5832.gj.243.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '243.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956904
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '243.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.b1.a1', '81.c1.a1', '81.f1.a1', '81.g1.a1'], 'contains': ['486.d1.a1', '486.h1.a1', '486.i1.a1', '729.a1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8651, -1, 9196, -1, 9185, -1, 9510, -1], 'generators': [3, 18, 36, 216], 'label': '5832.gj.243.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1.a1', 'old_label': '243.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956905
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '243.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.d1.a1', '81.e1.a1', '81.f1.a1', '81.h1.a1', '81.i1.a1'], 'contains': ['486.e1.a1', '486.j1.a1', '486.k1.a1', '729.a1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8499, -1, 8360, -1, 7949, -1, 9186, -1], 'generators': [3, 18, 36, 1944], 'label': '5832.gj.243.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.d1.a1', 'old_label': '243.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956906
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '243.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.g1.a1', '81.h1.a1'], 'contains': ['486.g1.a1', '486.p1.a1', '486.q1.a1', '729.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [9674, -1, 8988, -1, 9758, -1, 9926, -1], 'generators': [3, 18, 36, 24], 'label': '5832.gj.243.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.e1.a1', 'old_label': '243.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956907
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '108.d1.a1', '108.e1.a1', '108.f1.a1', '108.g1.a1', '108.h1.a1', '108.i1.a1', '162.l1.a1', '162.r1.a1', '162.s1.a1'], 'contains': ['648.a1.a1', '972.a1.a1', '972.b1.a1', '972.c1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6604, 6496, 7269, 5040, 4719, 7030, 6929, 6950], 'generators': [36, 216, 1944], 'label': '5832.gj.324.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '324.a1.a1', 'normal_contained_in': ['108.a1.a1', '108.b1.a1'], 'normal_contains': ['648.a1.a1', '972.a1.a1', '972.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '4.2', 'quotient_action_kernel': '81.12', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 227956908
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.j1.a1', '162.b1.a1'], 'contains': ['648.b1.a1', '972.a1.a1', '972.d1.a1', '972.f1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3849, -1, 6678, -1, 5301, -1, 6063, -1], 'generators': [36, 2, 216], 'label': '5832.gj.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '324.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956909
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': ['2916.b1.b1', '2916.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.a1', '6.e1.a1', '6.j1.a1', '6.k1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7535, 6487, 7432, 7988, 6048, 7234, 7935, 8552], 'generators': [21, 24, 4392, 2, 36, 1944, 4104, 1152], 'label': '5832.gj.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.b1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '972.445'}
  • id: 227956910
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.g1.a1'], 'contains': ['24.d1.a1', '36.p1.a1', '36.q1.a1', '36.q1.b1', '36.q1.c1', '36.s1.a1', '36.s2.a1', '36.v1.a1', '36.y1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1930, -1, 1556, -1, 1473, -1, 1597, -1], 'generators': [39, 2160, 1944, 2, 288, 3768], 'label': '5832.gj.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '12.j1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956911
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.j1.a1', '108.k1.a1', '108.k2.a1', '162.c1.a1', '162.t1.a1', '162.u1.a1'], 'contains': ['648.c1.a1', '972.a1.a1', '972.e1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6952, -1, 9186, -1, 7436, -1, 7460, -1], 'generators': [36, 578, 216], 'label': '5832.gj.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '324.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956912
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.j1.a1', '162.d1.a1', '162.v1.a1', '162.w1.a1'], 'contains': ['648.d1.a1', '972.a1.a1', '972.g1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7058, -1, 8441, -1, 6433, -1, 7301, -1], 'generators': [36, 288, 216], 'label': '5832.gj.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '324.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956913
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '108.k1.a1', '108.k2.a1', '162.m1.a1', '162.x1.a1', '162.y1.a1'], 'contains': ['648.e1.a1', '972.a1.a1', '972.h1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9070, -1, 9603, -1, 8072, -1, 8768, -1], 'generators': [36, 24, 216], 'label': '5832.gj.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '324.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956914
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '108.k1.a1', '108.k2.a1', '162.z1.a1'], 'contains': ['648.f1.a1', '972.a1.a1', '972.i1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9294, -1, 9822, -1, 8157, -1, 8709, -1], 'generators': [36, 26, 216], 'label': '5832.gj.324.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1.a1', 'old_label': '324.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956915
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.l1.a1', '162.e1.a1'], 'contains': ['648.g1.a1', '972.b1.a1', '972.d1.a1', '972.f1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3932, -1, 7066, -1, 4908, -1, 6004, -1], 'generators': [36, 2, 1944], 'label': '5832.gj.324.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '324.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956916
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.l1.a1', '108.m1.a1', '108.m2.a1', '162.f1.a1', '162.ba1.a1', '162.bb1.a1'], 'contains': ['648.h1.a1', '972.b1.a1', '972.e1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6031, -1, 8210, -1, 5731, -1, 7145, -1], 'generators': [36, 578, 1944], 'label': '5832.gj.324.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '324.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956917
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.l1.a1', '108.n1.a1', '108.o1.a1', '162.g1.a1', '162.bc1.a1', '162.bd1.a1'], 'contains': ['648.i1.a1', '972.b1.a1', '972.g1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7229, -1, 7986, -1, 6347, -1, 7242, -1], 'generators': [36, 288, 1944], 'label': '5832.gj.324.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '324.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956918
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '108.n1.a1', '162.n1.a1', '162.be1.a1', '162.bf1.a1'], 'contains': ['648.j1.a1', '972.b1.a1', '972.h1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7689, -1, 8065, -1, 6609, -1, 7814, -1], 'generators': [36, 24, 1944], 'label': '5832.gj.324.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '324.j1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956919
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '108.o1.a1', '162.bg1.a1'], 'contains': ['648.k1.a1', '972.b1.a1', '972.i1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8094, -1, 8716, -1, 6695, -1, 7519, -1], 'generators': [36, 26, 1944], 'label': '5832.gj.324.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1.a1', 'old_label': '324.k1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956920
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.h1.a1', '108.m1.a1', '108.m2.a1', '162.o1.a1', '162.bh1.a1', '162.bi1.a1'], 'contains': ['648.l1.a1', '972.b1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6316, -1, 7470, -1, 5661, -1, 7194, -1], 'generators': [36, 5040, 1944], 'label': '5832.gj.324.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '324.l1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956921
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.g1.a1'], 'contains': ['24.d1.a1', '36.p1.b1', '36.q1.d1', '36.q1.e1', '36.q1.f1', '36.s1.b1', '36.s2.b1', '36.v1.b1', '36.y1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1930, -1, 1177, -1, 1473, -1, 1081, -1], 'generators': [3, 2160, 1944, 2, 288, 3768], 'label': '5832.gj.12.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '12.j1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.b1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227956922
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.i1.a1', '108.m1.a1', '108.m2.a1', '162.bj1.a1'], 'contains': ['648.m1.a1', '972.b1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6408, -1, 7573, -1, 5560, -1, 7411, -1], 'generators': [36, 1154, 1944], 'label': '5832.gj.324.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '324.m1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.m1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956923
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.p1.a1', '108.q1.a1', '108.q1.b1', '108.q1.c1', '108.q2.a1', '108.q2.b1', '108.q2.c1', '108.t1.a1', '162.h1.a1'], 'contains': ['648.n1.a1', '972.c1.a1', '972.d1.a1', '972.f1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2765, -1, 4057, -1, 2859, -1, 3819, -1], 'generators': [36, 2, 2160], 'label': '5832.gj.324.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '324.n1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956941
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.z1.a1', '108.ba1.a1', '108.bb1.a1', '162.a1.a1'], 'contains': ['648.x1.a1', '972.j1.a1', '972.k1.a1', '972.l1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2332, -1, 6965, -1, 4041, -1, 5014, -1], 'generators': [39, 2, 4392], 'label': '5832.gj.324.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.z1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956924
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.r1.a1', '108.s1.a1', '108.s1.b1', '108.s1.c1', '108.t1.a1', '162.i1.a1'], 'contains': ['648.o1.a1', '972.c1.a1', '972.d1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2553, -1, 2551, -1, 3213, -1, 3937, -1], 'generators': [36, 2, 4104], 'label': '5832.gj.324.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '324.o1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956925
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.p1.a1', '108.t1.a1', '108.u1.a1', '108.u1.b1', '108.u1.c1', '108.u2.a1', '108.u2.b1', '108.u2.c1', '162.j1.a1'], 'contains': ['648.p1.a1', '972.c1.a1', '972.e1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2635, -1, 3879, -1, 2990, -1, 3761, -1], 'generators': [36, 578, 4104], 'label': '5832.gj.324.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '324.p1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956926
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.p1.a1', '108.v1.a1', '108.w1.a1', '108.w1.b1', '108.w1.c1'], 'contains': ['648.q1.a1', '972.c1.a1', '972.f1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3132, -1, 4830, -1, 3350, -1, 3995, -1], 'generators': [36, 1946, 4104], 'label': '5832.gj.324.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '324.q1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.q1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956927
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.p1.a1', '108.t1.a1', '108.x1.a1', '108.x1.b1', '108.x1.c1', '108.y1.a1', '108.y1.b1', '108.y1.c1', '162.k1.a1'], 'contains': ['648.r1.a1', '972.c1.a1', '972.g1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2891, -1, 4636, -1, 3076, -1, 3878, -1], 'generators': [36, 288, 4104], 'label': '5832.gj.324.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '324.r1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956928
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1.a1', '108.r1.a1', '108.v1.a1', '162.p1.a1'], 'contains': ['648.s1.a1', '972.c1.a1', '972.h1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4497, -1, 7385, -1, 5130, -1, 5497, -1], 'generators': [36, 24, 4104], 'label': '5832.gj.324.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '324.s1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.s1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956929
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1.a1', '108.r1.a1', '108.v1.a1'], 'contains': ['648.t1.a1', '972.c1.a1', '972.i1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4718, -1, 7320, -1, 4994, -1, 5438, -1], 'generators': [36, 26, 4104], 'label': '5832.gj.324.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '324.t1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.t1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956930
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '108.q1.a1', '108.q2.a1', '108.s1.a1', '108.u1.a1', '108.u2.a1', '108.w1.a1', '108.x1.a1', '108.x1.b1', '162.q1.a1'], 'contains': ['648.u1.a1', '972.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1222, -1, 2642, -1, 1094, -1, 2420, -1], 'generators': [36, 5784, 2160], 'label': '5832.gj.324.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '324.u1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956931
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '108.q1.b1', '108.q2.b1', '108.s1.b1', '108.u1.b1', '108.u2.b1', '108.w1.b1', '108.x1.a1', '108.x1.c1', '162.q1.b1'], 'contains': ['648.u1.b1', '972.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1222, -1, 2458, -1, 1094, -1, 2911, -1], 'generators': [36, 3840, 2160], 'label': '5832.gj.324.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '324.u1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.u1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956932
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.h1.a1'], 'contains': ['24.b1.a1', '36.p1.a1', '36.t1.a1', '36.w1.a1', '36.z1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3403, -1, 5481, -1, 3383, -1, 5809, -1], 'generators': [39, 1944, 4104, 2, 288, 3096], 'label': '5832.gj.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.k1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956933
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.f1.a1', '108.q1.c1', '108.q2.c1', '108.s1.c1', '108.u1.c1', '108.u2.c1', '108.w1.c1', '108.x1.b1', '108.x1.c1', '162.q1.c1'], 'contains': ['648.u1.c1', '972.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1222, -1, 3557, -1, 1094, -1, 2695, -1], 'generators': [36, 1896, 2160], 'label': '5832.gj.324.u1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '324.u1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.u1.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227956934
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '108.q1.b1', '108.q1.c1', '108.q2.a1', '108.s1.b1', '108.u1.b1', '108.u1.c1', '108.u2.a1', '108.w1.a1', '108.w1.c1', '108.y1.a1', '108.y1.b1'], 'contains': ['648.v1.a1', '972.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1278, -1, 4343, -1, 1149, -1, 3341, -1], 'generators': [36, 1178, 4104], 'label': '5832.gj.324.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '324.v1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.v1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956935
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '108.q1.a1', '108.q1.c1', '108.q2.b1', '108.s1.c1', '108.u1.a1', '108.u1.c1', '108.u2.b1', '108.w1.a1', '108.w1.b1', '108.y1.a1', '108.y1.c1'], 'contains': ['648.v1.b1', '972.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1278, -1, 4265, -1, 1149, -1, 3447, -1], 'generators': [36, 3122, 4104], 'label': '5832.gj.324.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '324.v1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.v1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956936
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '108.q1.a1', '108.q1.b1', '108.q2.c1', '108.s1.a1', '108.u1.a1', '108.u1.b1', '108.u2.c1', '108.w1.b1', '108.w1.c1', '108.y1.b1', '108.y1.c1'], 'contains': ['648.v1.c1', '972.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1278, -1, 4529, -1, 1149, -1, 3199, -1], 'generators': [36, 5066, 4104], 'label': '5832.gj.324.v1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '324.v1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.v1.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227956937
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.l1.a1', '108.p1.a1', '108.t1.a1'], 'contains': ['648.w1.a1', '972.d1.a1', '972.e1.a1', '972.f1.a1', '972.g1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4346, -1, 8146, -1, 5216, -1, 6419, -1], 'generators': [36, 2, 288], 'label': '5832.gj.324.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '324.w1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.w1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227956938
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.l1.a1', '108.t1.a1', '162.a1.a1', '162.bk1.a1', '162.bl1.a1'], 'contains': ['648.x1.a1', '972.d1.a1', '972.e1.a1', '972.g1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5432, -1, 8492, -1, 6074, -1, 6659, -1], 'generators': [36, 4106, 288], 'label': '5832.gj.324.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.x1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956939
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.l1.a1', '108.p1.a1', '162.bm1.a1'], 'contains': ['648.y1.a1', '972.e1.a1', '972.f1.a1', '972.g1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5271, -1, 8651, -1, 6159, -1, 6811, -1], 'generators': [36, 3890, 288], 'label': '5832.gj.324.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '324.y1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956940
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.y2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.j1.a1', '108.l1.a1', '108.p1.a1', '162.bn1.a1'], 'contains': ['648.y2.a1', '972.e1.a1', '972.f1.a1', '972.g1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5514, -1, 8586, -1, 5988, -1, 6870, -1], 'generators': [36, 218, 288], 'label': '5832.gj.324.y2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '324.y2.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.y2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956942
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.z1.b1', '108.ba1.b1', '108.bb1.b1', '162.a1.a1'], 'contains': ['648.x1.a1', '972.j1.b1', '972.k1.b1', '972.l1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2332, -1, 5753, -1, 4041, -1, 4767, -1], 'generators': [3, 2, 4392], 'label': '5832.gj.324.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.z1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.z1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956943
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.h1.a1'], 'contains': ['24.b1.a1', '36.p1.b1', '36.t1.b1', '36.w1.b1', '36.z1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3403, -1, 5060, -1, 3383, -1, 5747, -1], 'generators': [3, 1944, 4104, 2, 288, 3096], 'label': '5832.gj.12.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.k1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.b1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227956944
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.z1.a1', '108.bc1.a1', '162.b1.a1'], 'contains': ['648.b1.a1', '972.j1.a1', '972.m1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2122, -1, 6519, -1, 4269, -1, 5073, -1], 'generators': [39, 2, 216], 'label': '5832.gj.324.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '324.ba1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956945
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.z1.b1', '108.bc1.b1', '162.b1.a1'], 'contains': ['648.b1.a1', '972.j1.b1', '972.m1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2122, -1, 5688, -1, 4269, -1, 4825, -1], 'generators': [3, 2, 216], 'label': '5832.gj.324.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '324.ba1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956946
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.z1.a1', '108.bd1.a1', '108.bf1.a1', '162.c1.a1'], 'contains': ['648.c1.a1', '972.k1.a1', '972.m1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4013, -1, 7530, -1, 5387, -1, 5945, -1], 'generators': [39, 2306, 216], 'label': '5832.gj.324.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '324.bb1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956947
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.z1.b1', '108.bd1.b1', '108.bf1.b1', '162.c1.a1'], 'contains': ['648.c1.a1', '972.k1.b1', '972.m1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4013, -1, 6433, -1, 5387, -1, 5887, -1], 'generators': [3, 2306, 216], 'label': '5832.gj.324.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '324.bb1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956948
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.z1.a1', '108.be1.a1', '162.d1.a1'], 'contains': ['648.d1.a1', '972.l1.a1', '972.m1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4095, -1, 7016, -1, 4582, -1, 5829, -1], 'generators': [39, 4392, 216], 'label': '5832.gj.324.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '324.bc1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956949
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.z1.b1', '108.be1.b1', '162.d1.a1'], 'contains': ['648.d1.a1', '972.l1.b1', '972.m1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4095, -1, 5925, -1, 4582, -1, 5556, -1], 'generators': [3, 4392, 216], 'label': '5832.gj.324.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '324.bc1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956950
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ba1.a1', '108.bc1.a1', '162.e1.a1'], 'contains': ['648.g1.a1', '972.j1.a1', '972.n1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2204, -1, 6787, -1, 3715, -1, 4955, -1], 'generators': [39, 2, 1944], 'label': '5832.gj.324.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '324.bd1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956951
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ba1.b1', '108.bc1.b1', '162.e1.a1'], 'contains': ['648.g1.a1', '972.j1.b1', '972.n1.b1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2204, -1, 5804, -1, 3715, -1, 4708, -1], 'generators': [3, 2, 1944], 'label': '5832.gj.324.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '324.bd1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956952
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ba1.a1', '108.bd1.a1', '108.bg1.a1', '162.f1.a1'], 'contains': ['648.h1.a1', '972.k1.a1', '972.n1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3490, -1, 7118, -1, 3956, -1, 5712, -1], 'generators': [39, 2306, 1944], 'label': '5832.gj.324.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '324.be1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.be1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956953
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ba1.b1', '108.bd1.b1', '108.bg1.b1', '162.f1.a1'], 'contains': ['648.h1.a1', '972.k1.b1', '972.n1.b1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3490, -1, 6060, -1, 3956, -1, 5344, -1], 'generators': [3, 2306, 1944], 'label': '5832.gj.324.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '324.be1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.be1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956954
    {'ambient': '5832.gj', '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': '972.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.e1.a1', '6.k1.a1', '9.d1.a1'], 'contains': ['36.b1.a1', '54.u1.a1', '54.w1.a1', '54.bk1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8314, 7951, 7732, 8490, 6826, 9324, 8864, 9399], 'generators': [21, 1944, 216, 36, 24, 4176], 'label': '5832.gj.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.b1.a1', '6.e1.a1'], 'normal_contains': ['36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '2916.ef', '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': '972.445'}
  • id: 227956955
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ba1.a1', '108.be1.a1', '108.bh1.a1', '162.g1.a1'], 'contains': ['648.i1.a1', '972.l1.a1', '972.n1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3697, -1, 6913, -1, 4498, -1, 5770, -1], 'generators': [39, 4392, 1944], 'label': '5832.gj.324.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '324.bf1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956956
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.ba1.b1', '108.be1.b1', '108.bh1.b1', '162.g1.a1'], 'contains': ['648.i1.a1', '972.l1.b1', '972.n1.b1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3697, -1, 5975, -1, 4498, -1, 5654, -1], 'generators': [3, 4392, 1944], 'label': '5832.gj.324.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '324.bf1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227956957
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bb1.a1', '108.bc1.a1', '108.bi1.a1', '108.bi1.b1', '108.bi1.c1', '162.h1.a1'], 'contains': ['648.n1.a1', '972.j1.a1', '972.o1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1085, -1, 1393, -1, 2415, -1, 3554, -1], 'generators': [39, 2, 2160], 'label': '5832.gj.324.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '324.bg1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956958
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bb1.b1', '108.bc1.b1', '108.bi1.d1', '108.bi1.e1', '108.bi1.f1', '162.h1.a1'], 'contains': ['648.n1.a1', '972.j1.b1', '972.o1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1085, -1, 190, -1, 2415, -1, 2230, -1], 'generators': [3, 2, 2160], 'label': '5832.gj.324.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '324.bg1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956959
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bb1.a1', '108.bc1.a1', '108.bj1.a1', '108.bk1.a1', '108.bk1.b1', '108.bk1.c1', '162.i1.a1'], 'contains': ['648.o1.a1', '972.j1.a1', '972.o1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [980, -1, 1460, -1, 2722, -1, 3612, -1], 'generators': [39, 2, 4104], 'label': '5832.gj.324.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '324.bh1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956960
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bb1.b1', '108.bc1.b1', '108.bj1.b1', '108.bk1.d1', '108.bk1.e1', '108.bk1.f1', '162.i1.a1'], 'contains': ['648.o1.a1', '972.j1.b1', '972.o1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [980, -1, 792, -1, 2722, -1, 2288, -1], 'generators': [3, 2, 4104], 'label': '5832.gj.324.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '324.bh1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956961
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bb1.a1', '108.bd1.a1', '108.bl1.a1', '108.bl1.b1', '108.bl1.c1', '162.j1.a1'], 'contains': ['648.p1.a1', '972.k1.a1', '972.o1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1634, -1, 842, -1, 2553, -1, 3495, -1], 'generators': [39, 2306, 4104], 'label': '5832.gj.324.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '324.bi1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956962
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bb1.b1', '108.bd1.b1', '108.bl1.d1', '108.bl1.e1', '108.bl1.f1', '162.j1.a1'], 'contains': ['648.p1.a1', '972.k1.b1', '972.o1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1634, -1, 113, -1, 2553, -1, 2172, -1], 'generators': [3, 2306, 4104], 'label': '5832.gj.324.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '324.bi1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956963
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bb1.a1', '108.be1.a1', '108.bm1.a1', '108.bm1.b1', '108.bm1.c1', '162.k1.a1'], 'contains': ['648.r1.a1', '972.l1.a1', '972.o1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1924, -1, 1702, -1, 2637, -1, 3671, -1], 'generators': [39, 4392, 4104], 'label': '5832.gj.324.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '324.bj1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956964
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bb1.b1', '108.be1.b1', '108.bm1.d1', '108.bm1.e1', '108.bm1.f1', '162.k1.a1'], 'contains': ['648.r1.a1', '972.l1.b1', '972.o1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1924, -1, 1651, -1, 2637, -1, 2347, -1], 'generators': [3, 4392, 4104], 'label': '5832.gj.324.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '324.bj1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956965
    {'ambient': '5832.gj', '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': '972.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.l1.a1', '9.e1.a1'], 'contains': ['36.c1.a1', '54.t1.a1', '54.y1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7710, 6415, 8166, 6210, 6557, 5018, 7584, 6880], 'generators': [18, 1944, 216, 36, 3096, 504], 'label': '5832.gj.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.c1.a1', '6.d1.a1'], 'normal_contains': ['36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '2916.ef', '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': '972.446'}
  • id: 227956966
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bc1.a1', '108.bd1.a1', '108.be1.a1', '108.bn1.a1', '108.bo1.a1', '108.bp1.a1', '162.l1.a1'], 'contains': ['648.a1.a1', '972.m1.a1', '972.n1.a1', '972.o1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3559, -1, 5460, -1, 3421, -1, 5605, -1], 'generators': [39, 216, 1944], 'label': '5832.gj.324.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.bk1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956967
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bc1.b1', '108.bd1.b1', '108.be1.b1', '108.bn1.b1', '108.bo1.b1', '108.bp1.b1', '162.l1.a1'], 'contains': ['648.a1.a1', '972.m1.b1', '972.n1.b1', '972.o1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3559, -1, 5147, -1, 3421, -1, 5181, -1], 'generators': [3, 216, 1944], 'label': '5832.gj.324.bk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.bk1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956968
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bf1.a1', '108.bn1.a1', '162.m1.a1'], 'contains': ['648.e1.a1', '972.m1.a1', '972.p1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5340, -1, 7824, -1, 6231, -1, 7096, -1], 'generators': [39, 24, 216], 'label': '5832.gj.324.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '324.bl1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956969
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bf1.b1', '108.bn1.b1', '162.m1.a1'], 'contains': ['648.e1.a1', '972.m1.b1', '972.p1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5340, -1, 7650, -1, 6231, -1, 7056, -1], 'generators': [3, 24, 216], 'label': '5832.gj.324.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '324.bl1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956970
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bh1.a1', '108.bn1.a1', '162.n1.a1'], 'contains': ['648.j1.a1', '972.n1.a1', '972.p1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5014, -1, 6871, -1, 5504, -1, 7017, -1], 'generators': [39, 24, 1944], 'label': '5832.gj.324.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.g1.a1', 'old_label': '324.bm1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956971
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bh1.b1', '108.bn1.b1', '162.n1.a1'], 'contains': ['648.j1.a1', '972.n1.b1', '972.p1.b1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5014, -1, 6233, -1, 5504, -1, 6978, -1], 'generators': [3, 24, 1944], 'label': '5832.gj.324.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.g1.a1', 'old_label': '324.bm1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bm1.b1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227956972
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bg1.a1', '108.bp1.a1', '162.o1.a1'], 'contains': ['648.l1.a1', '972.n1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4237, -1, 6840, -1, 3890, -1, 6256, -1], 'generators': [39, 1152, 1944], 'label': '5832.gj.324.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '324.bn1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956973
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bg1.b1', '108.bp1.b1', '162.o1.a1'], 'contains': ['648.l1.a1', '972.n1.b1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4237, -1, 6293, -1, 3890, -1, 6166, -1], 'generators': [3, 1152, 1944], 'label': '5832.gj.324.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '324.bn1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956974
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bj1.a1', '108.bn1.a1', '162.p1.a1'], 'contains': ['648.s1.a1', '972.o1.a1', '972.p1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4164, -1, 5846, -1, 4836, -1, 5295, -1], 'generators': [39, 24, 4104], 'label': '5832.gj.324.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1.a1', 'old_label': '324.bo1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956975
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bj1.b1', '108.bn1.b1', '162.p1.a1'], 'contains': ['648.s1.a1', '972.o1.b1', '972.p1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4164, -1, 5592, -1, 4836, -1, 5256, -1], 'generators': [3, 24, 4104], 'label': '5832.gj.324.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.k1.a1', 'old_label': '324.bo1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227956976
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.g1.a1', '6.h1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.p1.a1', '36.p1.b1', '54.a1.a1', '54.b1.a1', '54.c1.a1', '54.d1.a1', '54.e1.a1', '54.f1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3898, -1, 6187, -1, 4657, -1, 6117, -1], 'generators': [3, 1944, 4104, 36, 2, 288], 'label': '5832.gj.18.c1.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.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227956977
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bi1.a1', '108.bk1.a1', '108.bl1.a1', '108.bm1.a1', '108.bo1.a1', '162.q1.a1'], 'contains': ['648.u1.a1', '972.o1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [312, -1, 688, -1, 306, -1, 1553, -1], 'generators': [39, 3552, 2160], 'label': '5832.gj.324.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '324.bp1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956978
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bi1.b1', '108.bk1.b1', '108.bl1.b1', '108.bm1.c1', '108.bo1.a1', '162.q1.b1'], 'contains': ['648.u1.b1', '972.o1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [312, -1, 1248, -1, 306, -1, 1860, -1], 'generators': [39, 1608, 2160], 'label': '5832.gj.324.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '324.bp1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956979
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bi1.c1', '108.bk1.c1', '108.bl1.c1', '108.bm1.b1', '108.bo1.a1', '162.q1.c1'], 'contains': ['648.u1.c1', '972.o1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [312, -1, 1829, -1, 306, -1, 1606, -1], 'generators': [39, 5496, 2160], 'label': '5832.gj.324.bp1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '324.bp1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bp1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956980
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bi1.d1', '108.bk1.d1', '108.bl1.d1', '108.bm1.d1', '108.bo1.b1', '162.q1.a1'], 'contains': ['648.u1.a1', '972.o1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [312, -1, 152, -1, 306, -1, 1385, -1], 'generators': [3, 3552, 2160], 'label': '5832.gj.324.bp1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '324.bp1.d1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bp1.d1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956981
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bi1.e1', '108.bk1.e1', '108.bl1.e1', '108.bm1.f1', '108.bo1.b1', '162.q1.b1'], 'contains': ['648.u1.b1', '972.o1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [312, -1, 360, -1, 306, -1, 1487, -1], 'generators': [3, 1608, 2160], 'label': '5832.gj.324.bp1.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '324.bp1.e1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bp1.e1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956982
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '324.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bi1.f1', '108.bk1.f1', '108.bl1.f1', '108.bm1.e1', '108.bo1.b1', '162.q1.c1'], 'contains': ['648.u1.c1', '972.o1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [312, -1, 999, -1, 306, -1, 1416, -1], 'generators': [3, 5496, 2160], 'label': '5832.gj.324.bp1.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '324.bp1.f1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.bp1.f1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956983
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1.a1', '162.b1.a1', '162.e1.a1', '162.h1.a1', '162.i1.a1'], 'contains': ['972.d1.a1', '972.j1.a1', '972.j1.b1', '1458.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [3599, -1, 6634, -1, 4412, -1, 5132, -1], 'generators': [3, 36, 2], 'label': '5832.gj.486.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '486.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227956984
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1.a1', '162.c1.a1', '162.f1.a1', '162.j1.a1', '243.a1.a1'], 'contains': ['972.e1.a1', '972.k1.a1', '972.k1.b1', '1458.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5662, -1, 7902, -1, 5817, -1, 6301, -1], 'generators': [3, 36, 2306], 'label': '5832.gj.486.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '486.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227956985
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1.a1', '162.d1.a1', '162.g1.a1', '162.k1.a1', '243.b1.a1'], 'contains': ['972.g1.a1', '972.l1.a1', '972.l1.b1', '1458.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5768, -1, 7954, -1, 5903, -1, 6360, -1], 'generators': [3, 36, 4392], 'label': '5832.gj.486.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '486.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956986
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.b1.a1', '162.c1.a1', '162.d1.a1', '162.l1.a1', '162.m1.a1', '243.c1.a1'], 'contains': ['972.a1.a1', '972.m1.a1', '972.m1.b1', '1458.a1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6494, -1, 8551, -1, 6282, -1, 6766, -1], 'generators': [3, 36, 216], 'label': '5832.gj.486.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '486.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956987
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1'], 'contains': ['36.o1.a1', '36.q1.a1', '36.q1.d1', '54.c1.a1', '54.j1.a1', '54.l1.a1', '54.m1.a1', '54.n1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1130, -1, 742, -1, 831, -1, 1803, -1], 'generators': [3, 2160, 3552, 36, 2, 2232], 'label': '5832.gj.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '18.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956988
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.e1.a1', '162.f1.a1', '162.g1.a1', '162.l1.a1', '162.n1.a1', '162.o1.a1', '243.d1.a1'], 'contains': ['972.b1.a1', '972.n1.a1', '972.n1.b1', '1458.a1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6268, -1, 7395, -1, 5611, -1, 6735, -1], 'generators': [3, 36, 1944], 'label': '5832.gj.486.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '486.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956989
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.h1.a1', '162.i1.a1', '162.j1.a1', '162.k1.a1', '162.l1.a1', '162.p1.a1', '162.q1.a1', '162.q1.b1', '162.q1.c1'], 'contains': ['972.c1.a1', '972.o1.a1', '972.o1.b1', '1458.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [2533, -1, 1409, -1, 2925, -1, 3715, -1], 'generators': [3, 36, 4104], 'label': '5832.gj.486.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '486.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956990
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.m1.a1', '162.n1.a1', '162.p1.a1', '243.e1.a1'], 'contains': ['972.h1.a1', '972.p1.a1', '972.p1.b1', '1458.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [6926, -1, 8107, -1, 6760, -1, 7647, -1], 'generators': [3, 36, 24], 'label': '5832.gj.486.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.e1.a1', 'old_label': '486.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956991
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.r1.a1', '162.t1.a1', '162.v1.a1', '162.x1.a1', '162.z1.a1', '243.c1.a1'], 'contains': ['972.a1.a1', '1458.b1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8914, -1, 9219, -1, 9232, -1, 9102, -1], 'generators': [18, 216, 36], 'label': '5832.gj.486.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '486.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956992
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.bh2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.s1.a1', '162.u1.a1', '162.w1.a1', '162.y1.a1', '243.c1.a1'], 'contains': ['972.a1.a1', '1458.c1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8377, -1, 9157, -1, 7871, -1, 9312, -1], 'generators': [21, 36, 216], 'label': '5832.gj.486.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '486.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956993
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.be2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.r1.a1', '162.ba1.a1', '162.bc1.a1', '162.be1.a1', '162.bg1.a1', '162.bh1.a1', '243.d1.a1'], 'contains': ['972.b1.a1', '1458.b1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8555, -1, 8218, -1, 8000, -1, 8827, -1], 'generators': [18, 36, 1944], 'label': '5832.gj.486.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '486.j1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956994
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.bi1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.s1.a1', '162.bb1.a1', '162.bd1.a1', '162.bf1.a1', '162.bi1.a1', '162.bj1.a1', '243.d1.a1'], 'contains': ['972.b1.a1', '1458.c1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7873, -1, 7674, -1, 7366, -1, 8621, -1], 'generators': [21, 1944, 36], 'label': '5832.gj.486.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '486.k1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227956995
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.t1.a1', '162.ba1.a1', '162.bk1.a1', '162.bm1.a1', '243.a1.a1'], 'contains': ['972.e1.a1', '1458.b1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [7556, -1, 9253, -1, 8631, -1, 8333, -1], 'generators': [18, 2522, 36], 'label': '5832.gj.486.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.b1.a1', 'old_label': '486.l1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227956996
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.u1.a1', '162.bb1.a1', '162.bl1.a1', '162.bn1.a1', '243.a1.a1'], 'contains': ['972.e1.a1', '1458.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [7407, -1, 9054, -1, 7784, -1, 8563, -1], 'generators': [21, 362, 36], 'label': '5832.gj.486.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.d1.a1', 'old_label': '486.m1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227956997
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.v1.a1', '162.bc1.a1', '162.bk1.a1', '162.bm1.a1', '243.b1.a1'], 'contains': ['972.g1.a1', '1458.b1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8177, -1, 8923, -1, 8688, -1, 8524, -1], 'generators': [18, 36, 504], 'label': '5832.gj.486.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '486.n1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227956998
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1'], 'contains': ['36.o1.b1', '36.q1.b1', '36.q1.e1', '54.c1.a1', '54.j1.c1', '54.l1.c1', '54.m1.c1', '54.n1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1130, -1, 1457, -1, 831, -1, 1973, -1], 'generators': [3, 2160, 5496, 36, 2, 2232], 'label': '5832.gj.18.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '18.d1.b1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.b1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227956999
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.w1.a1', '162.bd1.a1', '162.bl1.a1', '162.bn1.a1', '243.b1.a1'], 'contains': ['972.g1.a1', '1458.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7819, -1, 8888, -1, 7727, -1, 8660, -1], 'generators': [21, 36, 4176], 'label': '5832.gj.486.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '486.o1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957000
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.x1.a1', '162.be1.a1', '243.e1.a1'], 'contains': ['972.h1.a1', '1458.b1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9703, -1, 9021, -1, 9385, -1, 9648, -1], 'generators': [18, 24, 36], 'label': '5832.gj.486.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.g1.a1', 'old_label': '486.p1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957001
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '486.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.y1.a1', '162.bf1.a1', '243.e1.a1'], 'contains': ['972.h1.a1', '1458.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9255, -1, 8987, -1, 8746, -1, 9720, -1], 'generators': [21, 36, 24], 'label': '5832.gj.486.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.h1.a1', 'old_label': '486.q1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.q1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957002
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '486.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.z1.a1', '162.bg1.a1'], 'contains': ['972.i1.a1', '1458.b1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [9776, -1, 9839, -1, 9551, -1, 9463, -1], 'generators': [18, 4490, 36], 'label': '5832.gj.486.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.z1.a1', 'old_label': '486.r1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.r1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957003
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.d1.a1', '216.e1.a1', '216.f1.a1', '216.g1.a1', '216.h1.a1', '216.i1.a1', '324.a1.a1', '324.bk1.a1', '324.bk1.b1'], 'contains': ['1944.a1.a1', '1944.b1.a1', '1944.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4605, 5718, 5228, 4347, 3536, 6173, 5602, 6188], 'generators': [216, 1944], 'label': '5832.gj.648.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['216.a1.a1', '216.b1.a1', '324.a1.a1'], 'normal_contains': ['1944.a1.a1', '1944.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '4.2', 'quotient_action_kernel': '162.48', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 227957004
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '216.j1.a1', '324.b1.a1', '324.ba1.a1', '324.ba1.b1'], 'contains': ['1944.a1.a1', '1944.d1.a1', '1944.f1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2345, -1, 6068, -1, 4178, -1, 4969, -1], 'generators': [2, 216], 'label': '5832.gj.648.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '648.b1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957005
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.j1.a1', '216.k1.a1', '216.k2.a1', '324.c1.a1', '324.bb1.a1', '324.bb1.b1'], 'contains': ['1944.a1.a1', '1944.e1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5527, -1, 7429, -1, 5161, -1, 5992, -1], 'generators': [578, 216], 'label': '5832.gj.648.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '648.c1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957006
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '216.j1.a1', '324.d1.a1', '324.bc1.a1', '324.bc1.b1'], 'contains': ['1944.a1.a1', '1944.g1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4909, -1, 6390, -1, 4508, -1, 5637, -1], 'generators': [288, 216], 'label': '5832.gj.648.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '648.d1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227957007
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '216.k1.a1', '216.k2.a1', '324.e1.a1', '324.bl1.a1', '324.bl1.b1'], 'contains': ['1944.a1.a1', '1944.h1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9017, -1, 7666, -1, 6231, -1, 7076, -1], 'generators': [24, 216], 'label': '5832.gj.648.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '648.e1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227957008
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '216.k1.a1', '216.k2.a1', '324.f1.a1'], 'contains': ['1944.a1.a1', '1944.i1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9123, -1, 7835, -1, 6334, -1, 7247, -1], 'generators': [26, 216], 'label': '5832.gj.648.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.p1.a1', 'old_label': '648.f1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227957009
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1'], 'contains': ['36.o1.c1', '36.q1.c1', '36.q1.f1', '54.c1.a1', '54.j1.b1', '54.l1.b1', '54.m1.b1', '54.n1.c1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1130, -1, 856, -1, 831, -1, 2508, -1], 'generators': [3, 2160, 1608, 36, 2, 2232], 'label': '5832.gj.18.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.c1', 'old_label': '18.d1.c1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.c1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227957010
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '216.l1.a1', '324.g1.a1', '324.bd1.a1', '324.bd1.b1'], 'contains': ['1944.b1.a1', '1944.d1.a1', '1944.f1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2415, -1, 6244, -1, 3972, -1, 4898, -1], 'generators': [2, 1944], 'label': '5832.gj.648.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '648.g1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957011
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.l1.a1', '216.m1.a1', '216.m2.a1', '324.h1.a1', '324.be1.a1', '324.be1.b1'], 'contains': ['1944.b1.a1', '1944.e1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4461, -1, 6511, -1, 4230, -1, 5704, -1], 'generators': [578, 1944], 'label': '5832.gj.648.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '648.h1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957012
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '216.l1.a1', '216.n1.a1', '216.o1.a1', '324.i1.a1', '324.bf1.a1', '324.bf1.b1'], 'contains': ['1944.b1.a1', '1944.g1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4852, -1, 6450, -1, 4611, -1, 5770, -1], 'generators': [288, 1944], 'label': '5832.gj.648.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '648.i1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227957013
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '216.n1.a1', '324.j1.a1', '324.bm1.a1', '324.bm1.b1'], 'contains': ['1944.b1.a1', '1944.h1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5832, -1, 6481, -1, 5222, -1, 6945, -1], 'generators': [24, 1944], 'label': '5832.gj.648.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '648.j1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 227957014
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '216.o1.a1', '324.k1.a1'], 'contains': ['1944.b1.a1', '1944.i1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7005, -1, 6900, -1, 5293, -1, 6560, -1], 'generators': [26, 1944], 'label': '5832.gj.648.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.u1.a1', 'old_label': '648.k1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957015
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.z1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.h1.a1', '216.m1.a1', '216.m2.a1', '324.l1.a1', '324.bn1.a1', '324.bn1.b1'], 'contains': ['1944.b1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5101, -1, 6744, -1, 4323, -1, 6256, -1], 'generators': [5040], 'label': '5832.gj.648.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '648.l1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227957016
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.ba1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.i1.a1', '216.m1.a1', '216.m2.a1', '324.m1.a1'], 'contains': ['1944.b1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5144, -1, 6772, -1, 4278, -1, 6468, -1], 'generators': [1154], 'label': '5832.gj.648.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '648.m1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.m1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227957017
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '216.p1.a1', '216.q1.a1', '216.q1.b1', '216.q1.c1', '216.q2.a1', '216.q2.b1', '216.q2.c1', '216.t1.a1', '324.n1.a1', '324.bg1.a1', '324.bg1.b1'], 'contains': ['1944.c1.a1', '1944.d1.a1', '1944.f1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1507, -1, 2852, -1, 2748, -1, 2107, -1], 'generators': [2, 2160], 'label': '5832.gj.648.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '648.n1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957018
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '216.r1.a1', '216.s1.a1', '216.s1.b1', '216.s1.c1', '216.t1.a1', '324.o1.a1', '324.bh1.a1', '324.bh1.b1'], 'contains': ['1944.c1.a1', '1944.d1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1401, -1, 1907, -1, 3093, -1, 2255, -1], 'generators': [2, 4104], 'label': '5832.gj.648.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '648.o1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957019
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.p1.a1', '216.t1.a1', '216.u1.a1', '216.u1.b1', '216.u1.c1', '216.u2.a1', '216.u2.b1', '216.u2.c1', '324.p1.a1', '324.bi1.a1', '324.bi1.b1'], 'contains': ['1944.c1.a1', '1944.e1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1793, -1, 2729, -1, 2800, -1, 2071, -1], 'generators': [578, 4104], 'label': '5832.gj.648.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '648.p1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957020
    {'ambient': '5832.gj', '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': '2916.a1.a1', 'complements': ['1944.d1.a1', '1944.f1.a1', '1944.e1.a1', '1944.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.d1.a1', '6.e1.a1', '9.d1.a1', '9.e1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7184, 3085, 7524, 6849, 6238, 3485, 7686, 6817], 'generators': [3, 3096, 288, 18, 24, 1944, 216, 36], 'label': '5832.gj.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.e1.a1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '2916.ef', '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': '2916.ef'}
  • id: 227957021
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['36.d1.a1', '36.r1.a1', '36.r1.b1', '54.d1.a1', '54.k1.a1', '54.o1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4144, -1, 6326, -1, 4792, -1, 5675, -1], 'generators': [3, 1944, 4104, 36, 2, 24], 'label': '5832.gj.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '18.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '486.103'}
  • id: 227957022
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '216.p1.a1', '216.v1.a1', '216.w1.a1', '216.w1.b1', '216.w1.c1', '324.q1.a1'], 'contains': ['1944.c1.a1', '1944.f1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1954, -1, 3979, -1, 3144, -1, 2178, -1], 'generators': [1946, 4104], 'label': '5832.gj.648.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '648.q1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.q1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227957023
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '216.p1.a1', '216.t1.a1', '216.x1.a1', '216.x1.b1', '216.x1.c1', '216.y1.a1', '216.y1.b1', '216.y1.c1', '324.r1.a1', '324.bj1.a1', '324.bj1.b1'], 'contains': ['1944.c1.a1', '1944.g1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2023, -1, 3444, -1, 2851, -1, 2142, -1], 'generators': [288, 4104], 'label': '5832.gj.648.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '648.r1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957024
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '216.r1.a1', '216.v1.a1', '324.s1.a1', '324.bo1.a1', '324.bo1.b1'], 'contains': ['1944.c1.a1', '1944.h1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4296, -1, 5744, -1, 4836, -1, 5275, -1], 'generators': [24, 4104], 'label': '5832.gj.648.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '648.s1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.s1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227957025
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '216.r1.a1', '216.v1.a1', '324.t1.a1'], 'contains': ['1944.c1.a1', '1944.i1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4667, -1, 5782, -1, 4559, -1, 5163, -1], 'generators': [26, 4104], 'label': '5832.gj.648.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '648.t1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.t1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227957026
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '216.q1.a1', '216.q2.a1', '216.s1.a1', '216.u1.a1', '216.u2.a1', '216.w1.a1', '216.x1.a1', '216.x1.b1', '324.u1.a1', '324.bp1.a1', '324.bp1.d1'], 'contains': ['1944.c1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [346, -1, 1851, -1, 908, -1, 1112, -1], 'generators': [5784], 'label': '5832.gj.648.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '648.u1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227957027
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '216.q1.b1', '216.q2.b1', '216.s1.b1', '216.u1.b1', '216.u2.b1', '216.w1.b1', '216.x1.a1', '216.x1.c1', '324.u1.b1', '324.bp1.b1', '324.bp1.e1'], 'contains': ['1944.c1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [346, -1, 2022, -1, 908, -1, 1300, -1], 'generators': [3840], 'label': '5832.gj.648.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '648.u1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.u1.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227957028
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.f1.a1', '216.q1.c1', '216.q2.c1', '216.s1.c1', '216.u1.c1', '216.u2.c1', '216.w1.c1', '216.x1.b1', '216.x1.c1', '324.u1.c1', '324.bp1.c1', '324.bp1.f1'], 'contains': ['1944.c1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [346, -1, 2251, -1, 908, -1, 1152, -1], 'generators': [1896], 'label': '5832.gj.648.u1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '648.u1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.u1.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227957029
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1.a1', '216.q1.b1', '216.q1.c1', '216.q2.a1', '216.s1.b1', '216.u1.b1', '216.u1.c1', '216.u2.a1', '216.w1.a1', '216.w1.c1', '216.y1.a1', '216.y1.b1', '324.v1.a1'], 'contains': ['1944.c1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [657, -1, 3368, -1, 1009, -1, 708, -1], 'generators': [1178], 'label': '5832.gj.648.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '648.v1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.v1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227957030
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1.a1', '216.q1.a1', '216.q1.c1', '216.q2.b1', '216.s1.c1', '216.u1.a1', '216.u1.c1', '216.u2.b1', '216.w1.a1', '216.w1.b1', '216.y1.a1', '216.y1.c1', '324.v1.b1'], 'contains': ['1944.c1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [657, -1, 3169, -1, 1009, -1, 973, -1], 'generators': [3122], 'label': '5832.gj.648.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '648.v1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.v1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227957031
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.g1.a1', '216.q1.a1', '216.q1.b1', '216.q2.c1', '216.s1.a1', '216.u1.a1', '216.u1.b1', '216.u2.c1', '216.w1.b1', '216.w1.c1', '216.y1.b1', '216.y1.c1', '324.v1.c1'], 'contains': ['1944.c1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [657, -1, 3228, -1, 1009, -1, 676, -1], 'generators': [5066], 'label': '5832.gj.648.v1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '648.v1.c1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.v1.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 227957032
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1'], 'contains': ['36.e1.a1', '36.s1.a1', '36.s1.b1', '54.d1.a1', '54.j1.a1', '54.j1.b1', '54.j1.c1', '54.p1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1839, -1, 1265, -1, 1342, -1, 2154, -1], 'generators': [3, 2160, 1944, 36, 2, 3768], 'label': '5832.gj.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '18.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227957033
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1.a1', '216.l1.a1', '216.p1.a1', '216.t1.a1', '324.w1.a1'], 'contains': ['1944.d1.a1', '1944.e1.a1', '1944.f1.a1', '1944.g1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2792, -1, 6015, -1, 3920, -1, 4862, -1], 'generators': [2, 288], 'label': '5832.gj.648.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1.a1', 'old_label': '648.w1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.w1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957034
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1.a1', '216.l1.a1', '216.t1.a1', '324.x1.a1', '324.z1.a1', '324.z1.b1'], 'contains': ['1944.d1.a1', '1944.e1.a1', '1944.g1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2888, -1, 6287, -1, 4024, -1, 4933, -1], 'generators': [4106, 288], 'label': '5832.gj.648.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '648.x1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957035
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1.a1', '216.l1.a1', '216.p1.a1', '324.y1.a1'], 'contains': ['1944.e1.a1', '1944.f1.a1', '1944.g1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3339, -1, 6107, -1, 4127, -1, 5004, -1], 'generators': [3890, 288], 'label': '5832.gj.648.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.n1.a1', 'old_label': '648.y1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957036
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '648.y2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.j1.a1', '216.l1.a1', '216.p1.a1', '324.y2.a1'], 'contains': ['1944.e1.a1', '1944.f1.a1', '1944.g1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3247, -1, 6164, -1, 4075, -1, 5040, -1], 'generators': [218, 288], 'label': '5832.gj.648.y2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '648.y2.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.y2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957037
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '729.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '243.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['243.a1.a1', '243.b1.a1', '243.c1.a1', '243.d1.a1', '243.e1.a1'], 'contains': ['1458.a1.a1', '1458.b1.a1', '1458.c1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [8351, -1, 9015, -1, 8416, -1, 8879, -1], 'generators': [3, 18], 'label': '5832.gj.729.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.a1.a1', 'old_label': '729.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '729.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957038
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '324.b1.a1', '324.c1.a1', '324.d1.a1', '324.e1.a1', '324.f1.a1', '486.d1.a1', '486.h1.a1', '486.i1.a1'], 'contains': ['1944.a1.a1', '2916.a1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6884, 6897, 9159, 4625, 6433, 7344, 7301, 6726], 'generators': [36, 216], 'label': '5832.gj.972.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '972.a1.a1', 'normal_contained_in': ['324.a1.a1'], 'normal_contains': ['1944.a1.a1', '2916.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '972.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '2.1', 'quotient_action_kernel': '486.129', 'quotient_action_kernel_order': 486, 'quotient_fusion': None, 'short_label': '972.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957039
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '324.g1.a1', '324.h1.a1', '324.i1.a1', '324.j1.a1', '324.k1.a1', '324.l1.a1', '324.m1.a1', '486.e1.a1', '486.j1.a1', '486.k1.a1'], 'contains': ['1944.b1.a1', '2916.a1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6470, 5915, 7651, 5502, 5865, 6778, 7194, 7230], 'generators': [36, 1944], 'label': '5832.gj.972.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '972.b1.a1', 'normal_contained_in': ['324.a1.a1'], 'normal_contains': ['1944.b1.a1', '2916.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '972.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '2.1', 'quotient_action_kernel': '486.127', 'quotient_action_kernel_order': 486, 'quotient_fusion': None, 'short_label': '972.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957040
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '324.n1.a1', '324.o1.a1', '324.p1.a1', '324.q1.a1', '324.r1.a1', '324.s1.a1', '324.t1.a1', '324.u1.a1', '324.u1.b1', '324.u1.c1', '324.v1.a1', '324.v1.b1', '324.v1.c1', '486.f1.a1'], 'contains': ['1944.c1.a1', '2916.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3090, -1, 4557, -1, 3192, -1, 3761, -1], 'generators': [36, 4104], 'label': '5832.gj.972.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '324.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '972.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957041
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.b1.a1', '324.g1.a1', '324.n1.a1', '324.o1.a1', '324.w1.a1', '324.x1.a1', '486.a1.a1'], 'contains': ['1944.d1.a1', '2916.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3661, -1, 6660, -1, 4908, -1, 5568, -1], 'generators': [36, 2], 'label': '5832.gj.972.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '972.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957042
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.c1.a1', '324.h1.a1', '324.p1.a1', '324.w1.a1', '324.x1.a1', '324.y1.a1', '324.y2.a1', '486.b1.a1', '486.l1.a1', '486.m1.a1'], 'contains': ['1944.e1.a1', '2916.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5419, -1, 8255, -1, 5988, -1, 6818, -1], 'generators': [36, 578], 'label': '5832.gj.972.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '972.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957043
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.f2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1'], 'contains': ['36.e2.a1', '36.s2.a1', '36.s2.b1', '54.d1.a1', '54.l1.a1', '54.l1.b1', '54.l1.c1', '54.p1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1988, -1, 1343, -1, 1631, -1, 2244, -1], 'generators': [3, 2160, 1944, 36, 290, 3768], 'label': '5832.gj.18.f2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '18.f2.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f2.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227957044
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.b1.a1', '324.g1.a1', '324.n1.a1', '324.q1.a1', '324.w1.a1', '324.y1.a1', '324.y2.a1'], 'contains': ['1944.f1.a1', '2916.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3846, -1, 7168, -1, 5029, -1, 5958, -1], 'generators': [36, 218], 'label': '5832.gj.972.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '972.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957045
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.d1.a1', '324.i1.a1', '324.r1.a1', '324.w1.a1', '324.x1.a1', '324.y1.a1', '324.y2.a1', '486.c1.a1', '486.n1.a1', '486.o1.a1'], 'contains': ['1944.g1.a1', '2916.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5668, -1, 8172, -1, 6053, -1, 6856, -1], 'generators': [36, 288], 'label': '5832.gj.972.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '972.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957046
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.e1.a1', '324.j1.a1', '324.s1.a1', '486.g1.a1', '486.p1.a1', '486.q1.a1'], 'contains': ['1944.h1.a1', '2916.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9092, -1, 8436, -1, 6619, -1, 7712, -1], 'generators': [36, 24], 'label': '5832.gj.972.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.h1.a1', 'old_label': '972.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957047
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.f1.a1', '324.k1.a1', '324.t1.a1', '486.r1.a1'], 'contains': ['1944.i1.a1', '2916.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9284, -1, 9355, -1, 6685, -1, 7425, -1], 'generators': [36, 26], 'label': '5832.gj.972.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1.a1', 'old_label': '972.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957048
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.z1.a1', '324.ba1.a1', '324.bd1.a1', '324.bg1.a1', '324.bh1.a1', '486.a1.a1'], 'contains': ['1944.d1.a1', '2916.b1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [2230, -1, 6612, -1, 3872, -1, 5073, -1], 'generators': [39, 2], 'label': '5832.gj.972.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '972.j1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957049
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.z1.b1', '324.ba1.b1', '324.bd1.b1', '324.bg1.b1', '324.bh1.b1', '486.a1.a1'], 'contains': ['1944.d1.a1', '2916.b1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [2230, -1, 5671, -1, 3872, -1, 4796, -1], 'generators': [3, 2], 'label': '5832.gj.972.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '972.j1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.j1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957050
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.z1.a1', '324.bb1.a1', '324.be1.a1', '324.bi1.a1', '486.b1.a1'], 'contains': ['1944.e1.a1', '2916.b1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2809, -1, 7138, -1, 4414, -1, 5506, -1], 'generators': [39, 2306], 'label': '5832.gj.972.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '972.k1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957051
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.z1.b1', '324.bb1.b1', '324.be1.b1', '324.bi1.b1', '486.b1.a1'], 'contains': ['1944.e1.a1', '2916.b1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2809, -1, 5950, -1, 4414, -1, 5394, -1], 'generators': [3, 2306], 'label': '5832.gj.972.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '972.k1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.k1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957052
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.z1.a1', '324.bc1.a1', '324.bf1.a1', '324.bj1.a1', '486.c1.a1'], 'contains': ['1944.g1.a1', '2916.b1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3024, -1, 7066, -1, 4459, -1, 5537, -1], 'generators': [39, 4392], 'label': '5832.gj.972.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '972.l1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957053
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.z1.b1', '324.bc1.b1', '324.bf1.b1', '324.bj1.b1', '486.c1.a1'], 'contains': ['1944.g1.a1', '2916.b1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [3024, -1, 5842, -1, 4459, -1, 5475, -1], 'generators': [3, 4392], 'label': '5832.gj.972.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '972.l1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957054
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1'], 'contains': ['36.f1.a1', '36.t1.a1', '36.t1.b1', '54.d1.a1', '54.q1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4870, -1, 5553, -1, 4152, -1, 6298, -1], 'generators': [3, 1944, 4104, 36, 2, 3096], 'label': '5832.gj.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '18.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '486.105'}
  • id: 227957055
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ba1.a1', '324.bb1.a1', '324.bc1.a1', '324.bk1.a1', '324.bl1.a1', '486.d1.a1'], 'contains': ['1944.a1.a1', '2916.b1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4083, -1, 7209, -1, 5075, -1, 5834, -1], 'generators': [39, 216], 'label': '5832.gj.972.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '972.m1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.m1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957056
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bk1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.ba1.b1', '324.bb1.b1', '324.bc1.b1', '324.bk1.b1', '324.bl1.b1', '486.d1.a1'], 'contains': ['1944.a1.a1', '2916.b1.b1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4083, -1, 6471, -1, 5075, -1, 5737, -1], 'generators': [3, 216], 'label': '5832.gj.972.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '972.m1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.m1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957057
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bd1.a1', '324.be1.a1', '324.bf1.a1', '324.bk1.a1', '324.bm1.a1', '324.bn1.a1', '486.e1.a1'], 'contains': ['1944.b1.a1', '2916.b1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3615, -1, 6952, -1, 4369, -1, 5803, -1], 'generators': [39, 1944], 'label': '5832.gj.972.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '972.n1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957058
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '162.bl1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bd1.b1', '324.be1.b1', '324.bf1.b1', '324.bk1.b1', '324.bm1.b1', '324.bn1.b1', '486.e1.a1'], 'contains': ['1944.b1.a1', '2916.b1.b1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3615, -1, 5878, -1, 4369, -1, 5670, -1], 'generators': [3, 1944], 'label': '5832.gj.972.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '972.n1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.n1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957059
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bg1.a1', '324.bh1.a1', '324.bi1.a1', '324.bj1.a1', '324.bk1.a1', '324.bo1.a1', '324.bp1.a1', '324.bp1.b1', '324.bp1.c1', '486.f1.a1'], 'contains': ['1944.c1.a1', '2916.b1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1747, -1, 1596, -1, 2908, -1, 3583, -1], 'generators': [39, 4104], 'label': '5832.gj.972.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '972.o1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957060
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bg1.b1', '324.bh1.b1', '324.bi1.b1', '324.bj1.b1', '324.bk1.b1', '324.bo1.b1', '324.bp1.d1', '324.bp1.e1', '324.bp1.f1', '486.f1.a1'], 'contains': ['1944.c1.a1', '2916.b1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1747, -1, 1371, -1, 2908, -1, 2288, -1], 'generators': [3, 4104], 'label': '5832.gj.972.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '972.o1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.o1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957061
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bl1.a1', '324.bm1.a1', '324.bo1.a1', '486.g1.a1'], 'contains': ['1944.h1.a1', '2916.b1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [5148, -1, 7338, -1, 5494, -1, 7013, -1], 'generators': [39, 24], 'label': '5832.gj.972.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.e1.a1', 'old_label': '972.p1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957062
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '972.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.bl1.b1', '324.bm1.b1', '324.bo1.b1', '486.g1.a1'], 'contains': ['1944.h1.a1', '2916.b1.b1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [5148, -1, 6570, -1, 5494, -1, 6978, -1], 'generators': [3, 24], 'label': '5832.gj.972.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.e1.a1', 'old_label': '972.p1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.p1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 227957063
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1458.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['486.a1.a1', '486.b1.a1', '486.c1.a1', '486.d1.a1', '486.e1.a1', '486.f1.a1', '486.g1.a1', '729.a1.a1'], 'contains': ['2916.a1.a1', '2916.b1.a1', '2916.b1.b1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5771, -1, 7914, -1, 5817, -1, 6360, -1], 'generators': [3, 36], 'label': '5832.gj.1458.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1458.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957064
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1458.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['486.h1.a1', '486.j1.a1', '486.l1.a1', '486.n1.a1', '486.p1.a1', '486.r1.a1', '729.a1.a1'], 'contains': ['2916.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8486, -1, 9108, -1, 8660, -1, 8827, -1], 'generators': [18], 'label': '5832.gj.1458.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '1458.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957065
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.b1.a1'], 'contains': ['36.g1.a1', '36.u1.a1', '36.u1.b1', '54.e1.a1', '54.g1.a1', '54.o1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6409, -1, 7804, -1, 6110, -1, 7196, -1], 'generators': [3, 1944, 4104, 36, 578, 24], 'label': '5832.gj.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227957066
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1458.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '27.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['486.i1.a1', '486.k1.a1', '486.m1.a1', '486.o1.a1', '486.q1.a1', '729.a1.a1'], 'contains': ['2916.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7927, -1, 9015, -1, 7784, -1, 8859, -1], 'generators': [21], 'label': '5832.gj.1458.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '1458.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1458.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957067
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '648.b1.a1', '648.c1.a1', '648.d1.a1', '648.e1.a1', '648.f1.a1', '972.a1.a1', '972.m1.a1', '972.m1.b1'], 'contains': ['5832.a1.a1'], 'core': '1944.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5096, 6826, 7202, 4259, 5075, 6755, 5826, 6201], 'generators': [216], 'label': '5832.gj.1944.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1944.a1.a1', 'normal_contained_in': ['648.a1.a1', '972.a1.a1'], 'normal_contains': ['5832.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1944.a1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '2.1', 'quotient_action_kernel': '972.313', 'quotient_action_kernel_order': 972, 'quotient_fusion': None, 'short_label': '1944.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957068
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1944.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '648.g1.a1', '648.h1.a1', '648.i1.a1', '648.j1.a1', '648.k1.a1', '648.l1.a1', '648.m1.a1', '972.b1.a1', '972.n1.a1', '972.n1.b1'], 'contains': ['5832.a1.a1'], 'core': '1944.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4856, 5505, 6548, 5438, 4346, 6189, 5778, 6705], 'generators': [1944], 'label': '5832.gj.1944.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1944.b1.a1', 'normal_contained_in': ['648.a1.a1', '972.b1.a1'], 'normal_contains': ['5832.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1944.b1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '2.1', 'quotient_action_kernel': '972.311', 'quotient_action_kernel_order': 972, 'quotient_fusion': None, 'short_label': '1944.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957069
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1944.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '648.n1.a1', '648.o1.a1', '648.p1.a1', '648.q1.a1', '648.r1.a1', '648.s1.a1', '648.t1.a1', '648.u1.a1', '648.u1.b1', '648.u1.c1', '648.v1.a1', '648.v1.b1', '648.v1.c1', '972.c1.a1', '972.o1.a1', '972.o1.b1'], 'contains': ['5832.a1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1931, -1, 2823, -1, 3093, -1, 2160, -1], 'generators': [4104], 'label': '5832.gj.1944.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '648.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '1944.c1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957070
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1944.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.b1.a1', '648.g1.a1', '648.n1.a1', '648.o1.a1', '648.w1.a1', '648.x1.a1', '972.d1.a1', '972.j1.a1', '972.j1.b1'], 'contains': ['5832.a1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2335, -1, 6000, -1, 3972, -1, 4915, -1], 'generators': [2], 'label': '5832.gj.1944.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '1944.d1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957071
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1944.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.c1.a1', '648.h1.a1', '648.p1.a1', '648.w1.a1', '648.x1.a1', '648.y1.a1', '648.y2.a1', '972.e1.a1', '972.k1.a1', '972.k1.b1'], 'contains': ['5832.a1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3167, -1, 6392, -1, 4178, -1, 5394, -1], 'generators': [578], 'label': '5832.gj.1944.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '1944.e1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957072
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1944.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.b1.a1', '648.g1.a1', '648.n1.a1', '648.q1.a1', '648.w1.a1', '648.y1.a1', '648.y2.a1', '972.f1.a1'], 'contains': ['5832.a1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2724, -1, 6078, -1, 4075, -1, 4969, -1], 'generators': [218], 'label': '5832.gj.1944.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '1944.f1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957073
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1944.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.d1.a1', '648.i1.a1', '648.r1.a1', '648.w1.a1', '648.x1.a1', '648.y1.a1', '648.y2.a1', '972.g1.a1', '972.l1.a1', '972.l1.b1'], 'contains': ['5832.a1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3237, -1, 6336, -1, 4262, -1, 5475, -1], 'generators': [288], 'label': '5832.gj.1944.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '1944.g1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957074
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1944.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.e1.a1', '648.j1.a1', '648.s1.a1', '972.h1.a1', '972.p1.a1', '972.p1.b1'], 'contains': ['5832.a1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6470, -1, 6737, -1, 5244, -1, 6961, -1], 'generators': [24], 'label': '5832.gj.1944.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.h1.a1', 'old_label': '1944.h1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 227957075
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '1944.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.f1.a1', '648.k1.a1', '648.t1.a1', '972.i1.a1'], 'contains': ['5832.a1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9209, -1, 7460, -1, 5293, -1, 6560, -1], 'generators': [26], 'label': '5832.gj.1944.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.x1.a1', 'old_label': '1944.i1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957076
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1'], 'contains': ['36.h1.a1', '36.v1.a1', '36.v1.b1', '54.e1.a1', '54.m1.a1', '54.m1.b1', '54.m1.c1', '54.p1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2234, -1, 1095, -1, 1789, -1, 2064, -1], 'generators': [3, 2160, 1944, 36, 578, 3768], 'label': '5832.gj.18.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '18.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227957077
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '2916.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': ['972.a1.a1', '972.b1.a1', '972.c1.a1', '972.d1.a1', '972.e1.a1', '972.f1.a1', '972.g1.a1', '972.h1.a1', '972.i1.a1', '1458.a1.a1', '1458.b1.a1', '1458.c1.a1'], 'contains': ['5832.a1.a1'], 'core': '2916.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5771, 6121, 8172, 4808, 5988, 7320, 6992, 7209], 'generators': [36], 'label': '5832.gj.2916.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '2916.a1.a1', 'normal_contained_in': ['972.a1.a1', '972.b1.a1'], 'normal_contains': ['5832.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2916.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2916.ef', 'quotient_action_kernel_order': 2916, 'quotient_fusion': None, 'short_label': '2916.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957078
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '2916.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.j1.a1', '972.k1.a1', '972.l1.a1', '972.m1.a1', '972.n1.a1', '972.o1.a1', '972.p1.a1', '1458.a1.a1'], 'contains': ['5832.a1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4045, -1, 7118, -1, 4414, -1, 5619, -1], 'generators': [39], 'label': '5832.gj.2916.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '2916.b1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957079
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '2916.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['972.j1.b1', '972.k1.b1', '972.l1.b1', '972.m1.b1', '972.n1.b1', '972.o1.b1', '972.p1.b1', '1458.a1.a1'], 'contains': ['5832.a1.a1'], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4045, -1, 5904, -1, 4414, -1, 5588, -1], 'generators': [3], 'label': '5832.gj.2916.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '2916.b1.b1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957080
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '5832.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': ['1944.a1.a1', '1944.b1.a1', '1944.c1.a1', '1944.d1.a1', '1944.e1.a1', '1944.f1.a1', '1944.g1.a1', '1944.h1.a1', '1944.i1.a1', '2916.a1.a1', '2916.b1.a1', '2916.b1.b1'], 'contains': [], 'core': '5832.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4045, 6121, 6431, 4808, 4346, 6755, 5604, 6705], 'generators': [], 'label': '5832.gj.5832.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '5832.a1.a1', 'normal_contained_in': ['1944.a1.a1', '1944.b1.a1', '2916.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '5832.a1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 227957081
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.c1.a1'], 'contains': ['36.i1.a1', '36.w1.a1', '36.w1.b1', '54.e1.a1', '54.h1.a1', '54.q1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5868, -1, 6801, -1, 4929, -1, 6669, -1], 'generators': [3, 1944, 4104, 36, 578, 3096], 'label': '5832.gj.18.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.j1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227957082
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.f1.a1', '9.d1.a1'], 'contains': ['36.b1.a1', '36.x1.a1', '36.x1.b1', '54.f1.a1', '54.i1.a1', '54.o1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6522, -1, 7300, -1, 5632, -1, 7021, -1], 'generators': [3, 1944, 4104, 36, 288, 24], 'label': '5832.gj.18.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.k1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227957083
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.g1.a1'], 'contains': ['36.k1.a1', '36.y1.a1', '36.y1.b1', '54.f1.a1', '54.n1.a1', '54.n1.b1', '54.n1.c1', '54.p1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2894, -1, 3289, -1, 1947, -1, 2353, -1], 'generators': [3, 2160, 1944, 36, 288, 3768], 'label': '5832.gj.18.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '18.l1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.a1', 'subgroup_fusion': None, 'weyl_group': '162.42'}
  • id: 227957084
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.h1.a1', '9.e1.a1'], 'contains': ['36.c1.a1', '36.z1.a1', '36.z1.b1', '54.f1.a1', '54.q1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6181, -1, 5925, -1, 4519, -1, 6383, -1], 'generators': [3, 1944, 4104, 36, 288, 3096], 'label': '5832.gj.18.m1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.m1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227957085
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.f1.a1', '6.i1.a1', '9.a1.a1', '9.b1.a1', '9.d1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8261, -1, 8334, -1, 7309, -1, 8429, -1], 'generators': [3, 24, 4392, 18, 36, 1944, 4104, 2], 'label': '5832.gj.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '972.428'}
  • id: 227957086
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.i1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '54.r1.a1', '54.t1.a1', '54.bb1.a1', '54.bf1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8165, -1, 8507, -1, 7919, -1, 8143, -1], 'generators': [18, 1944, 4392, 2, 216, 36], 'label': '5832.gj.18.n1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.n1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227957087
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.j1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '54.s1.a1', '54.u1.a1', '54.bc1.a1', '54.bg1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7821, -1, 8357, -1, 7067, -1, 8523, -1], 'generators': [21, 216, 4392, 2, 1944, 36], 'label': '5832.gj.18.o1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.o1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227957088
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.b1.a1'], 'contains': ['36.g1.a1', '54.r1.a1', '54.v1.a1', '54.x1.a1', '54.bd1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9150, -1, 9360, -1, 8557, -1, 9050, -1], 'generators': [18, 1944, 216, 578, 24, 36], 'label': '5832.gj.18.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.p1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 227957089
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.b1.a1'], 'contains': ['36.g1.a1', '54.s1.a1', '54.w1.a1', '54.be1.a1', '54.be2.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8946, -1, 8644, -1, 8191, -1, 9230, -1], 'generators': [21, 216, 24, 578, 1944, 36], 'label': '5832.gj.18.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.q1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 227957090
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.c1.a1'], 'contains': ['36.i1.a1', '54.r1.a1', '54.y1.a1', '54.bh1.a1', '54.bh2.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7494, -1, 8245, -1, 6666, -1, 7659, -1], 'generators': [18, 1944, 3096, 578, 216, 36], 'label': '5832.gj.18.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.r1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 227957091
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '9.c1.a1'], 'contains': ['36.i1.a1', '54.s1.a1', '54.z1.a1', '54.ba1.a1', '54.bi1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7352, -1, 7875, -1, 6231, -1, 7954, -1], 'generators': [21, 216, 1944, 578, 1152, 36], 'label': '5832.gj.18.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.s1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 227957092
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.i1.a1', '9.d1.a1'], 'contains': ['36.b1.a1', '54.t1.a1', '54.v1.a1', '54.bj1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8492, -1, 8058, -1, 8054, -1, 8776, -1], 'generators': [18, 1944, 504, 24, 216, 36], 'label': '5832.gj.18.t1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.t1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
  • id: 227957093
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.l1.a1'], 'contains': ['36.j1.a1', '54.t1.a1', '54.x1.a1', '54.bl1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8719, -1, 8725, -1, 8328, -1, 8615, -1], 'generators': [18, 1944, 2448, 26, 216, 36], 'label': '5832.gj.18.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '18.u1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
  • id: 227957094
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.j1.a1', '9.e1.a1'], 'contains': ['36.c1.a1', '54.u1.a1', '54.z1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7102, -1, 7156, -1, 6006, -1, 7880, -1], 'generators': [21, 216, 4176, 1152, 36, 1944], 'label': '5832.gj.18.v1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.v1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
  • id: 227957095
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '6.k1.a1'], 'contains': ['36.m1.a1', '54.u1.a1', '54.ba1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7620, -1, 7209, -1, 5917, -1, 8027, -1], 'generators': [21, 216, 3960, 1154, 36, 1944], 'label': '5832.gj.18.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '18.w1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
  • id: 227957096
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.c1.a1', '6.h1.a1', '6.j1.a1', '9.a1.a1', '9.c1.a1', '9.e1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7454, -1, 7690, -1, 6394, -1, 7793, -1], 'generators': [3, 3096, 4392, 18, 36, 1944, 216, 2], 'label': '5832.gj.3.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '3.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.a1', 'subgroup_fusion': None, 'weyl_group': '972.429'}
  • id: 227957097
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.i1.a1', '12.i1.b1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.d1.a1', '72.g1.a1', '72.j1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5244, 3924, 5866, 4538, 3949, 5552, 6011, 4544], 'generators': [2, 24, 288], 'label': '5832.gj.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['72.a1.a1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
  • id: 227957098
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': ['243.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.k1.a1', '12.k1.b1'], 'contains': ['72.a1.a1', '72.c1.a1', '72.f1.a1', '72.i1.a1', '72.m1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4700, 2915, 5132, 1279, 3218, 3179, 5611, 3753], 'generators': [2, 1152, 288], 'label': '5832.gj.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1'], 'normal_contains': ['72.a1.a1', '72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
  • id: 227957099
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': ['243.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.k1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4360, 1773, 4930, 2298, 2971, 2173, 5237, 2858], 'generators': [24, 1152], 'label': '5832.gj.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.a1.a1', '12.c1.a1', '12.d1.a1', '12.d1.b1'], 'normal_contains': ['72.b1.a1', '72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '12.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '324.117'}
  • id: 227957100
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.e1.a1', '12.j1.a1', '12.j1.b1'], 'contains': ['72.a1.a1', '72.e1.a1', '72.e2.a1', '72.h1.a1', '72.k1.a1', '72.l1.a1', '72.n1.a1', '72.n1.b1', '72.n1.c1', '72.o1.a1', '72.o1.b1', '72.o1.c1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1590, -1, 3046, -1, 1902, -1, 569, -1], 'generators': [2, 1464, 288, 1944], 'label': '5832.gj.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 227957101
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.f1.a1'], 'contains': ['72.b1.a1', '72.l1.a1', '72.m1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4956, -1, 5180, -1, 2881, -1, 5719, -1], 'generators': [1154, 24], 'label': '5832.gj.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.e1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
  • id: 227957102
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.g1.a1'], 'contains': ['72.j1.a1', '72.k1.a1', '72.l1.a1', '72.m1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3198, -1, 5040, -1, 2527, -1, 3908, -1], 'generators': [1154, 1464], 'label': '5832.gj.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 227957103
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.h1.a1'], 'contains': ['72.c1.a1', '72.j1.a1', '72.l1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4573, -1, 5233, -1, 3060, -1, 5449, -1], 'generators': [26, 1152], 'label': '5832.gj.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.g1.a1', 'projective_image': '5832.gj', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
  • id: 227957104
    {'ambient': '5832.gj', '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': '972.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['54.a1.a1', '54.bb1.a1', '54.bc1.a1', '81.a1.a1', '81.b1.a1', '81.c1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8143, -1, 8842, -1, 7778, -1, 8345, -1], 'generators': [3, 216, 4392, 18, 2, 36], 'label': '5832.gj.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '2916.ef', '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': '36.10'}
  • id: 227957105
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1'], 'contains': ['54.b1.a1', '54.bf1.a1', '54.bg1.a1', '81.a1.a1', '81.d1.a1', '81.e1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7997, -1, 8933, -1, 7329, -1, 8241, -1], 'generators': [3, 1944, 4392, 18, 2, 36], 'label': '5832.gj.27.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '27.b1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227957106
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.c1.a1'], 'contains': ['54.e1.a1', '54.r1.a1', '54.s1.a1', '81.b1.a1', '81.d1.a1', '81.f1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7845, -1, 8609, -1, 7560, -1, 8437, -1], 'generators': [3, 1944, 4104, 18, 578, 36], 'label': '5832.gj.27.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1.a1', 'old_label': '27.c1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227957107
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6197, 5379, 6834, 4044, 4021, 5214, 6522, 4649], 'generators': [36, 216, 288, 2, 1944, 24, 1152], 'label': '5832.gj.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.b1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '2916.ef', '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': '324.117'}
  • id: 227957108
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '972.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.d1.a1', '9.e1.a1'], 'contains': ['54.f1.a1', '54.t1.a1', '54.u1.a1', '81.c1.a1', '81.e1.a1', '81.f1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8516, -1, 8055, -1, 7453, -1, 8695, -1], 'generators': [3, 1944, 4104, 18, 36, 504], 'label': '5832.gj.27.d1.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.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.a1', 'subgroup_fusion': None, 'weyl_group': '108.40'}
  • id: 227957109
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '27.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1'], 'contains': ['54.g1.a1', '54.bd1.a1', '54.be2.a1', '81.b1.a1', '81.g1.a1'], 'core': '972.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9671, -1, 9409, -1, 9014, -1, 9471, -1], 'generators': [3, 216, 24, 18, 2522, 36], 'label': '5832.gj.27.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1.a1', 'old_label': '27.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 227957110
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '27.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1458.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1'], 'contains': ['54.h1.a1', '54.bh2.a1', '54.bi1.a1', '81.d1.a1', '81.i1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7375, -1, 8130, -1, 6456, -1, 7813, -1], 'generators': [3, 1944, 1152, 18, 2306, 36], 'label': '5832.gj.27.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.f1.a1', 'old_label': '27.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.f1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 227957111
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '27.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.a1'], 'contains': ['54.i1.a1', '54.bj1.a1', '54.bk1.a1', '81.e1.a1', '81.h1.a1'], 'core': '972.b1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8719, -1, 7987, -1, 7660, -1, 8962, -1], 'generators': [3, 1944, 4392, 18, 36, 24], 'label': '5832.gj.27.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.g1.a1', 'old_label': '27.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.g1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 227957112
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '27.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.d1.a1'], 'contains': ['54.o1.a1', '54.v1.a1', '54.w1.a1', '81.f1.a1', '81.g1.a1', '81.h1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9281, -1, 8474, -1, 8442, -1, 9152, -1], 'generators': [3, 1944, 216, 18, 36, 24], 'label': '5832.gj.27.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '27.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.h1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
  • id: 227957113
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '27.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2916.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '9.e1.a1'], 'contains': ['54.q1.a1', '54.y1.a1', '54.z1.a1', '81.f1.a1', '81.i1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7239, -1, 7930, -1, 6348, -1, 7739, -1], 'generators': [3, 1944, 216, 18, 36, 3096], 'label': '5832.gj.27.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '27.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.i1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 227957114
    {'ambient': '5832.gj', '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': '36.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.e1.a1', '18.c1.a1', '18.n1.a1', '18.o1.a1'], 'contains': ['72.a1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1', '108.j1.a1', '108.l1.a1', '108.p1.a1', '108.t1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4039, 8389, 6899, 5438, 4657, 8129, 6400, 8160], 'generators': [36, 1944, 2, 288, 216], 'label': '5832.gj.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1'], 'normal_contains': ['72.a1.a1', '108.a1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '2916.ef', 'quotient_action_image': '36.10', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 227957115
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.c1.a1', '12.f1.a1', '18.a1.a1', '18.k1.a1', '18.t1.a1'], 'contains': ['72.b1.a1', '108.b1.a1', '108.d1.a1', '108.n1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6675, 6826, 7314, 6833, 5634, 6755, 7208, 6936], 'generators': [36, 1944, 24, 288, 216], 'label': '5832.gj.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.a1.a1', '12.c1.a1', '18.a1.a1'], 'normal_contains': ['72.b1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '2916.ef', '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': '324.117'}
  • id: 227957116
    {'ambient': '5832.gj', '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': '324.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.h1.a1', '18.b1.a1', '18.m1.a1', '18.v1.a1'], 'contains': ['72.c1.a1', '108.b1.a1', '108.h1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6135, 5121, 6820, 3455, 4303, 4365, 6816, 5600], 'generators': [36, 1944, 1152, 288, 216], 'label': '5832.gj.36.c1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.c1.a1', 'normal_contained_in': ['12.b1.a1', '12.c1.a1', '18.b1.a1'], 'normal_contains': ['72.c1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '2916.ef', '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': '324.117'}
  • id: 227957117
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.e1.a1'], 'contains': ['72.d1.a1', '108.c1.a1', '108.d1.a1', '108.e1.a1', '108.r1.a1', '108.v1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4260, -1, 7064, -1, 4977, -1, 5792, -1], 'generators': [36, 4104, 2, 24, 1944], 'label': '5832.gj.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.d1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '54.12'}
  • id: 227957118
    {'ambient': '5832.gj', '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': '2916.a1.a1', 'complements': ['1458.b1.a1', '1458.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.d1.a1', '12.i1.a1', '12.j1.a1', '12.k1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3582, 701, 5389, 2020, 3338, 617, 5738, 549], 'generators': [39, 216, 288, 2, 1944, 24, 3096], 'label': '5832.gj.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '5832.gj', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2916.ef'}
  • id: 227957119
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.f1.a1'], 'contains': ['72.e1.a1', '108.c1.a1', '108.f1.a1', '108.g1.a1', '108.q1.a1', '108.q1.b1', '108.q1.c1', '108.q2.a1', '108.q2.b1', '108.q2.c1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1871, -1, 3819, -1, 1674, -1, 3012, -1], 'generators': [36, 2160, 2, 1464, 1944], 'label': '5832.gj.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.e1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 227957120
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.e2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.f2.a1'], 'contains': ['72.e2.a1', '108.c1.a1', '108.f1.a1', '108.g1.a1', '108.s1.a1', '108.s1.b1', '108.s1.c1', '108.w1.a1', '108.w1.b1', '108.w1.c1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2055, -1, 4096, -1, 2014, -1, 3161, -1], 'generators': [36, 2160, 290, 1464, 1944], 'label': '5832.gj.36.e2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.e2.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e2.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227957121
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.g1.a1'], 'contains': ['72.f1.a1', '108.c1.a1', '108.h1.a1', '108.i1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5638, -1, 5996, -1, 3612, -1, 6735, -1], 'generators': [36, 1944, 2, 1152, 4104], 'label': '5832.gj.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '36.f1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '54.12'}
  • id: 227957122
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.h1.a1', '18.p1.a1', '18.q1.a1'], 'contains': ['72.g1.a1', '108.a1.a1', '108.d1.a1', '108.e1.a1', '108.k1.a1', '108.k2.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7331, -1, 8287, -1, 6921, -1, 7567, -1], 'generators': [36, 216, 578, 24, 1944], 'label': '5832.gj.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.g1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 227957123
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.i1.a1'], 'contains': ['72.h1.a1', '108.a1.a1', '108.f1.a1', '108.g1.a1', '108.u1.a1', '108.u1.b1', '108.u1.c1', '108.u2.a1', '108.u2.b1', '108.u2.c1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2309, -1, 3565, -1, 2119, -1, 2936, -1], 'generators': [36, 2160, 578, 1464, 1944], 'label': '5832.gj.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.g1.a1', 'old_label': '36.h1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 227957124
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.j1.a1', '18.r1.a1', '18.s1.a1'], 'contains': ['72.i1.a1', '108.a1.a1', '108.h1.a1', '108.i1.a1', '108.m1.a1', '108.m2.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5959, -1, 7132, -1, 5161, -1, 7131, -1], 'generators': [36, 1944, 578, 1152, 216], 'label': '5832.gj.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.i1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 227957125
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.g1.a1', '12.h1.a1', '18.u1.a1'], 'contains': ['72.j1.a1', '108.b1.a1', '108.e1.a1', '108.o1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6840, -1, 7672, -1, 5512, -1, 7053, -1], 'generators': [36, 1944, 26, 288, 216], 'label': '5832.gj.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.j1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
  • id: 227957126
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.e1.a1', '12.g1.a1', '18.l1.a1'], 'contains': ['72.k1.a1', '108.b1.a1', '108.f1.a1', '108.x1.a1', '108.x1.b1', '108.x1.c1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2897, -1, 4505, -1, 2224, -1, 2790, -1], 'generators': [36, 2160, 1464, 288, 1944], 'label': '5832.gj.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.k1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '54.8'}
  • id: 227957127
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['72.l1.a1', '108.b1.a1', '108.g1.a1', '108.y1.a1', '108.y1.b1', '108.y1.c1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3057, -1, 5407, -1, 2379, -1, 3975, -1], 'generators': [36, 4104, 1178, 288, 1944], 'label': '5832.gj.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.l1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 227957128
    {'ambient': '5832.gj', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.f1.a1', '12.g1.a1', '18.w1.a1'], 'contains': ['72.m1.a1', '108.b1.a1', '108.i1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6249, -1, 6702, -1, 4044, -1, 6970, -1], 'generators': [36, 1944, 1154, 288, 216], 'label': '5832.gj.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '36.m1.a1', 'projective_image': '2916.ef', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}