Abstract group data - 648.496

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 18, 'aut_gen_orders': [6, 6, 6, 6, 6, 2], 'aut_gens': [[1, 6, 18, 108], [77, 516, 18, 180], [445, 228, 414, 144], [181, 264, 90, 144], [83, 258, 90, 180], [125, 294, 414, 144], [77, 294, 90, 540]], 'aut_group': None, 'aut_hash': 568666786874406346, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 23328, 'aut_permdeg': 62, 'aut_perms': [29373672400867267317886514128545866027437514980147689942280342137846922784822606795532, 21147460666415201791170333114728631202127646912889216053820420431574201923888895651646, 24240801165905435212923959974006765437674000894000211955113971957338632179181162060558, 15454229122179868239878575602727337616051536680270065814093303051205203893645838234926, 28874690499102192480800073583038213003645590228233741866415278533099432176082106331094, 9800197064251473979772807656074327419388510626710492621160547670283821698511722471251], 'aut_phi_ratio': 108.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 54, 1, 1], [3, 2, 1, 1], [3, 2, 3, 1], [3, 3, 2, 1], [3, 6, 2, 1], [3, 6, 3, 1], [3, 6, 6, 1], [4, 54, 1, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 2, 3, 1], [6, 2, 6, 1], [6, 3, 2, 1], [6, 6, 2, 2], [6, 6, 3, 1], [6, 6, 4, 1], [6, 6, 6, 2], [6, 6, 12, 1], [6, 54, 2, 1], [12, 54, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3^4.D_6^2.C_2', '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': '5832.et', 'autcentquo_hash': 7243380119719690966, 'autcentquo_nilpotent': False, 'autcentquo_order': 5832, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_3^3.S_3^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 54, 1], [3, 2, 4], [3, 3, 2], [3, 6, 11], [4, 54, 1], [6, 2, 12], [6, 3, 2], [6, 6, 35], [6, 54, 2], [12, 54, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '324.144', 'commutator_count': 1, 'commutator_label': '54.15', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 496, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 54, 1, 1], [3, 2, 1, 4], [3, 3, 2, 1], [3, 6, 1, 3], [3, 6, 2, 4], [4, 54, 1, 1], [6, 2, 1, 4], [6, 2, 2, 4], [6, 3, 2, 1], [6, 6, 1, 3], [6, 6, 2, 16], [6, 54, 2, 1], [12, 54, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4368, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '108.43', 'hash': 496, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [6, 3, 6, 3], 'inner_gens': [[1, 48, 414, 540], [85, 6, 18, 108], [361, 6, 18, 108], [217, 6, 18, 108]], 'inner_hash': 144, 'inner_nilpotent': False, 'inner_order': 324, 'inner_split': False, 'inner_tex': 'C_3^3:D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 12], [2, 51], [6, 12]], 'label': '648.496', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C3*C6^2):C6', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 75, 'number_divisions': 47, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 140, 'number_subgroup_classes': 283, 'number_subgroups': 1820, 'old_label': None, 'order': 648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 57], [3, 80], [4, 54], [6, 348], [12, 108]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[5, 6, 90, 108], [329, 78, 90, 612], [1, 474, 342, 108]], 'outer_group': '72.46', 'outer_hash': 46, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 8, 'outer_perms': [1, 724, 5784], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 13], [4, 21], [6, 6], [12, 3]], 'representations': {'PC': {'code': 3205407015333780986852603516146869, 'gens': [1, 3, 4, 6], 'pres': [7, -2, -3, -3, -2, -3, -2, -3, 14, 1010, 450, 11595, 80, 2524, 22685, 124, 21174]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [1166413, 1656953, 817163, 502525, 638221, 47089, 895013]}, 'Perm': {'d': 16, 'gens': [193117518985, 744, 269366590080, 1680, 1494615991683, 2897640748804, 2897640748800]}}, 'schur_multiplier': [3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_3\\times C_6^2):C_6', 'transitive_degree': 108, '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: 139786748
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 496, 'group_order': 648, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 139786759
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 496, 'group_order': 648, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 324, 'size': 1}
  • id: 139786770
    {'aut_label': '2B', 'centralizer': '2.a1', 'counter': 3, 'group_counter': 496, 'group_order': 648, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 54, 'size': 2}
  • id: 139786781
    {'aut_label': '2C', 'centralizer': '54.g1', 'counter': 4, 'group_counter': 496, 'group_order': 648, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 75, 'size': 54}
  • id: 139786792
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 496, 'group_order': 648, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 216, 'size': 2}
  • id: 139786803
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 6, 'group_counter': 496, 'group_order': 648, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 288, 'size': 2}
  • id: 139786814
    {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 496, 'group_order': 648, 'label': '3C', 'order': 3, 'powers': [7, 1], 'representative': 252, 'size': 2}
  • id: 139786821
    {'aut_label': '3D', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 496, 'group_order': 648, 'label': '3D', 'order': 3, 'powers': [8, 1], 'representative': 72, 'size': 2}
  • id: 139786822
    {'aut_label': '3E1', 'centralizer': '3.b1', 'counter': 9, 'group_counter': 496, 'group_order': 648, 'label': '3E1', 'order': 3, 'powers': [10, 1], 'representative': 40, 'size': 3}
  • id: 139786749
    {'aut_label': '3E1', 'centralizer': '3.b1', 'counter': 10, 'group_counter': 496, 'group_order': 648, 'label': '3E-1', 'order': 3, 'powers': [9, 1], 'representative': 74, 'size': 3}
  • id: 139786750
    {'aut_label': '3F', 'centralizer': '6.b1', 'counter': 11, 'group_counter': 496, 'group_order': 648, 'label': '3F', 'order': 3, 'powers': [11, 1], 'representative': 228, 'size': 6}
  • id: 139786751
    {'aut_label': '3F', 'centralizer': '6.b1', 'counter': 12, 'group_counter': 496, 'group_order': 648, 'label': '3G', 'order': 3, 'powers': [12, 1], 'representative': 222, 'size': 6}
  • id: 139786752
    {'aut_label': '3F', 'centralizer': '6.b1', 'counter': 13, 'group_counter': 496, 'group_order': 648, 'label': '3H', 'order': 3, 'powers': [13, 1], 'representative': 12, 'size': 6}
  • id: 139786753
    {'aut_label': '3I1', 'centralizer': '6.a1', 'counter': 14, 'group_counter': 496, 'group_order': 648, 'label': '3I1', 'order': 3, 'powers': [15, 1], 'representative': 220, 'size': 6}
  • id: 139786754
    {'aut_label': '3I1', 'centralizer': '6.a1', 'counter': 15, 'group_counter': 496, 'group_order': 648, 'label': '3I-1', 'order': 3, 'powers': [14, 1], 'representative': 434, 'size': 6}
  • id: 139786755
    {'aut_label': '3J1', 'centralizer': '6.f1', 'counter': 16, 'group_counter': 496, 'group_order': 648, 'label': '3J1', 'order': 3, 'powers': [17, 1], 'representative': 268, 'size': 6}
  • id: 139786756
    {'aut_label': '3J1', 'centralizer': '6.f1', 'counter': 17, 'group_counter': 496, 'group_order': 648, 'label': '3J-1', 'order': 3, 'powers': [16, 1], 'representative': 440, 'size': 6}
  • id: 139786757
    {'aut_label': '3J1', 'centralizer': '6.f1', 'counter': 18, 'group_counter': 496, 'group_order': 648, 'label': '3K1', 'order': 3, 'powers': [19, 1], 'representative': 88, 'size': 6}
  • id: 139786758
    {'aut_label': '3J1', 'centralizer': '6.f1', 'counter': 19, 'group_counter': 496, 'group_order': 648, 'label': '3K-1', 'order': 3, 'powers': [18, 1], 'representative': 80, 'size': 6}
  • id: 139786760
    {'aut_label': '3J1', 'centralizer': '6.f1', 'counter': 20, 'group_counter': 496, 'group_order': 648, 'label': '3L1', 'order': 3, 'powers': [21, 1], 'representative': 298, 'size': 6}
  • id: 139786761
    {'aut_label': '3J1', 'centralizer': '6.f1', 'counter': 21, 'group_counter': 496, 'group_order': 648, 'label': '3L-1', 'order': 3, 'powers': [20, 1], 'representative': 446, 'size': 6}
  • id: 139786762
    {'aut_label': '4A', 'centralizer': '54.m1', 'counter': 22, 'group_counter': 496, 'group_order': 648, 'label': '4A', 'order': 4, 'powers': [2, 22], 'representative': 129, 'size': 54}
  • id: 139786763
    {'aut_label': '6A', 'centralizer': '2.a1', 'counter': 23, 'group_counter': 496, 'group_order': 648, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 108, 'size': 2}
  • id: 139786764
    {'aut_label': '6A', 'centralizer': '2.a1', 'counter': 24, 'group_counter': 496, 'group_order': 648, 'label': '6B', 'order': 6, 'powers': [6, 2], 'representative': 144, 'size': 2}
  • id: 139786765
    {'aut_label': '6A', 'centralizer': '2.a1', 'counter': 25, 'group_counter': 496, 'group_order': 648, 'label': '6C', 'order': 6, 'powers': [7, 2], 'representative': 180, 'size': 2}
  • id: 139786766
    {'aut_label': '6D', 'centralizer': '2.a1', 'counter': 26, 'group_counter': 496, 'group_order': 648, 'label': '6D', 'order': 6, 'powers': [8, 2], 'representative': 360, 'size': 2}
  • id: 139786767
    {'aut_label': '6E1', 'centralizer': '2.a1', 'counter': 27, 'group_counter': 496, 'group_order': 648, 'label': '6E1', 'order': 6, 'powers': [8, 3], 'representative': 18, 'size': 2}
  • id: 139786768
    {'aut_label': '6E1', 'centralizer': '2.a1', 'counter': 28, 'group_counter': 496, 'group_order': 648, 'label': '6E-1', 'order': 6, 'powers': [8, 3], 'representative': 90, 'size': 2}
  • id: 139786769
    {'aut_label': '6F1', 'centralizer': '2.a1', 'counter': 29, 'group_counter': 496, 'group_order': 648, 'label': '6F1', 'order': 6, 'powers': [6, 3], 'representative': 234, 'size': 2}
  • id: 139786771
    {'aut_label': '6F1', 'centralizer': '2.a1', 'counter': 30, 'group_counter': 496, 'group_order': 648, 'label': '6F-1', 'order': 6, 'powers': [6, 3], 'representative': 558, 'size': 2}
  • id: 139786772
    {'aut_label': '6F1', 'centralizer': '2.a1', 'counter': 31, 'group_counter': 496, 'group_order': 648, 'label': '6G1', 'order': 6, 'powers': [7, 3], 'representative': 126, 'size': 2}
  • id: 139786773
    {'aut_label': '6F1', 'centralizer': '2.a1', 'counter': 32, 'group_counter': 496, 'group_order': 648, 'label': '6G-1', 'order': 6, 'powers': [7, 3], 'representative': 450, 'size': 2}
  • id: 139786774
    {'aut_label': '6F1', 'centralizer': '2.a1', 'counter': 33, 'group_counter': 496, 'group_order': 648, 'label': '6H1', 'order': 6, 'powers': [5, 3], 'representative': 270, 'size': 2}
  • id: 139786775
    {'aut_label': '6F1', 'centralizer': '2.a1', 'counter': 34, 'group_counter': 496, 'group_order': 648, 'label': '6H-1', 'order': 6, 'powers': [5, 3], 'representative': 486, 'size': 2}
  • id: 139786776
    {'aut_label': '6I1', 'centralizer': '3.b1', 'counter': 35, 'group_counter': 496, 'group_order': 648, 'label': '6I1', 'order': 6, 'powers': [9, 2], 'representative': 326, 'size': 3}
  • id: 139786777
    {'aut_label': '6I1', 'centralizer': '3.b1', 'counter': 36, 'group_counter': 496, 'group_order': 648, 'label': '6I-1', 'order': 6, 'powers': [10, 2], 'representative': 328, 'size': 3}
  • id: 139786778
    {'aut_label': '6J', 'centralizer': '6.b1', 'counter': 37, 'group_counter': 496, 'group_order': 648, 'label': '6J', 'order': 6, 'powers': [11, 2], 'representative': 114, 'size': 6}
  • id: 139786779
    {'aut_label': '6J', 'centralizer': '6.b1', 'counter': 38, 'group_counter': 496, 'group_order': 648, 'label': '6K', 'order': 6, 'powers': [12, 2], 'representative': 120, 'size': 6}
  • id: 139786780
    {'aut_label': '6J', 'centralizer': '6.b1', 'counter': 39, 'group_counter': 496, 'group_order': 648, 'label': '6L', 'order': 6, 'powers': [13, 2], 'representative': 330, 'size': 6}
  • id: 139786782
    {'aut_label': '6M1', 'centralizer': '6.b1', 'counter': 40, 'group_counter': 496, 'group_order': 648, 'label': '6M1', 'order': 6, 'powers': [13, 3], 'representative': 24, 'size': 6}
  • id: 139786783
    {'aut_label': '6M1', 'centralizer': '6.b1', 'counter': 41, 'group_counter': 496, 'group_order': 648, 'label': '6M-1', 'order': 6, 'powers': [13, 3], 'representative': 30, 'size': 6}
  • id: 139786784
    {'aut_label': '6N1', 'centralizer': '6.a1', 'counter': 42, 'group_counter': 496, 'group_order': 648, 'label': '6N1', 'order': 6, 'powers': [14, 2], 'representative': 110, 'size': 6}
  • id: 139786785
    {'aut_label': '6N1', 'centralizer': '6.a1', 'counter': 43, 'group_counter': 496, 'group_order': 648, 'label': '6N-1', 'order': 6, 'powers': [15, 2], 'representative': 112, 'size': 6}
  • id: 139786786
    {'aut_label': '6O1', 'centralizer': '6.a1', 'counter': 44, 'group_counter': 496, 'group_order': 648, 'label': '6O1', 'order': 6, 'powers': [9, 3], 'representative': 20, 'size': 6}
  • id: 139786787
    {'aut_label': '6O1', 'centralizer': '6.a1', 'counter': 45, 'group_counter': 496, 'group_order': 648, 'label': '6O-1', 'order': 6, 'powers': [10, 3], 'representative': 22, 'size': 6}
  • id: 139786788
    {'aut_label': '6M1', 'centralizer': '6.b1', 'counter': 46, 'group_counter': 496, 'group_order': 648, 'label': '6P1', 'order': 6, 'powers': [12, 3], 'representative': 240, 'size': 6}
  • id: 139786789
    {'aut_label': '6M1', 'centralizer': '6.b1', 'counter': 47, 'group_counter': 496, 'group_order': 648, 'label': '6P-1', 'order': 6, 'powers': [12, 3], 'representative': 462, 'size': 6}
  • id: 139786790
    {'aut_label': '6M1', 'centralizer': '6.b1', 'counter': 48, 'group_counter': 496, 'group_order': 648, 'label': '6Q1', 'order': 6, 'powers': [11, 3], 'representative': 132, 'size': 6}
  • id: 139786791
    {'aut_label': '6M1', 'centralizer': '6.b1', 'counter': 49, 'group_counter': 496, 'group_order': 648, 'label': '6Q-1', 'order': 6, 'powers': [11, 3], 'representative': 456, 'size': 6}
  • id: 139786793
    {'aut_label': '6R1', 'centralizer': '6.a1', 'counter': 50, 'group_counter': 496, 'group_order': 648, 'label': '6R1', 'order': 6, 'powers': [14, 3], 'representative': 236, 'size': 6}
  • id: 139786794
    {'aut_label': '6R1', 'centralizer': '6.a1', 'counter': 51, 'group_counter': 496, 'group_order': 648, 'label': '6R-1', 'order': 6, 'powers': [15, 3], 'representative': 454, 'size': 6}
  • id: 139786795
    {'aut_label': '6S1', 'centralizer': '6.f1', 'counter': 52, 'group_counter': 496, 'group_order': 648, 'label': '6S1', 'order': 6, 'powers': [16, 2], 'representative': 116, 'size': 6}
  • id: 139786796
    {'aut_label': '6S1', 'centralizer': '6.f1', 'counter': 53, 'group_counter': 496, 'group_order': 648, 'label': '6S-1', 'order': 6, 'powers': [17, 2], 'representative': 118, 'size': 6}
  • id: 139786797
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 54, 'group_counter': 496, 'group_order': 648, 'label': '6T1', 'order': 6, 'powers': [18, 3], 'representative': 26, 'size': 6}
  • id: 139786798
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 55, 'group_counter': 496, 'group_order': 648, 'label': '6T-1', 'order': 6, 'powers': [19, 3], 'representative': 34, 'size': 6}
  • id: 139786799
    {'aut_label': '6R1', 'centralizer': '6.a1', 'counter': 56, 'group_counter': 496, 'group_order': 648, 'label': '6U1', 'order': 6, 'powers': [14, 3], 'representative': 452, 'size': 6}
  • id: 139786800
    {'aut_label': '6R1', 'centralizer': '6.a1', 'counter': 57, 'group_counter': 496, 'group_order': 648, 'label': '6U-1', 'order': 6, 'powers': [15, 3], 'representative': 238, 'size': 6}
  • id: 139786801
    {'aut_label': '6S1', 'centralizer': '6.f1', 'counter': 58, 'group_counter': 496, 'group_order': 648, 'label': '6V1', 'order': 6, 'powers': [20, 2], 'representative': 122, 'size': 6}
  • id: 139786802
    {'aut_label': '6S1', 'centralizer': '6.f1', 'counter': 59, 'group_counter': 496, 'group_order': 648, 'label': '6V-1', 'order': 6, 'powers': [21, 2], 'representative': 124, 'size': 6}
  • id: 139786804
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 60, 'group_counter': 496, 'group_order': 648, 'label': '6W1', 'order': 6, 'powers': [18, 3], 'representative': 32, 'size': 6}
  • id: 139786805
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 61, 'group_counter': 496, 'group_order': 648, 'label': '6W-1', 'order': 6, 'powers': [19, 3], 'representative': 28, 'size': 6}
  • id: 139786806
    {'aut_label': '6S1', 'centralizer': '6.f1', 'counter': 62, 'group_counter': 496, 'group_order': 648, 'label': '6X1', 'order': 6, 'powers': [18, 2], 'representative': 332, 'size': 6}
  • id: 139786807
    {'aut_label': '6S1', 'centralizer': '6.f1', 'counter': 63, 'group_counter': 496, 'group_order': 648, 'label': '6X-1', 'order': 6, 'powers': [19, 2], 'representative': 334, 'size': 6}
  • id: 139786808
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 64, 'group_counter': 496, 'group_order': 648, 'label': '6Y1', 'order': 6, 'powers': [20, 3], 'representative': 242, 'size': 6}
  • id: 139786809
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 65, 'group_counter': 496, 'group_order': 648, 'label': '6Y-1', 'order': 6, 'powers': [21, 3], 'representative': 466, 'size': 6}
  • id: 139786810
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 66, 'group_counter': 496, 'group_order': 648, 'label': '6Z1', 'order': 6, 'powers': [16, 3], 'representative': 134, 'size': 6}
  • id: 139786811
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 67, 'group_counter': 496, 'group_order': 648, 'label': '6Z-1', 'order': 6, 'powers': [17, 3], 'representative': 460, 'size': 6}
  • id: 139786812
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 68, 'group_counter': 496, 'group_order': 648, 'label': '6AA1', 'order': 6, 'powers': [16, 3], 'representative': 458, 'size': 6}
  • id: 139786813
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 69, 'group_counter': 496, 'group_order': 648, 'label': '6AA-1', 'order': 6, 'powers': [17, 3], 'representative': 136, 'size': 6}
  • id: 139786815
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 70, 'group_counter': 496, 'group_order': 648, 'label': '6AB1', 'order': 6, 'powers': [21, 3], 'representative': 244, 'size': 6}
  • id: 139786816
    {'aut_label': '6T1', 'centralizer': '6.f1', 'counter': 71, 'group_counter': 496, 'group_order': 648, 'label': '6AB-1', 'order': 6, 'powers': [20, 3], 'representative': 464, 'size': 6}
  • id: 139786817
    {'aut_label': '6AC1', 'centralizer': '54.g1', 'counter': 72, 'group_counter': 496, 'group_order': 648, 'label': '6AC1', 'order': 6, 'powers': [10, 4], 'representative': 73, 'size': 54}
  • id: 139786818
    {'aut_label': '6AC1', 'centralizer': '54.g1', 'counter': 73, 'group_counter': 496, 'group_order': 648, 'label': '6AC-1', 'order': 6, 'powers': [9, 4], 'representative': 77, 'size': 54}
  • id: 139786819
    {'aut_label': '12A1', 'centralizer': '54.m1', 'counter': 74, 'group_counter': 496, 'group_order': 648, 'label': '12A1', 'order': 12, 'powers': [35, 22], 'representative': 451, 'size': 54}
  • id: 139786820
    {'aut_label': '12A1', 'centralizer': '54.m1', 'counter': 75, 'group_counter': 496, 'group_order': 648, 'label': '12A-1', 'order': 12, 'powers': [36, 22], 'representative': 131, 'size': 54}
• 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: 12776540
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.1a', '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], 'schur_index': 1}
  • id: 12776551
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.1b', '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], 'schur_index': 1}
  • id: 12776562
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.1c', '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], 'schur_index': 1}
  • id: 12776573
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.1d', '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], 'schur_index': 1}
  • id: 12776582
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12776583
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.1f', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, -1, -1, 1, -2, 1, 1, 1, -2, -1, 2, 2, 1, 1, 1, 2, 1, -2, 1, -1, 1, 1, 1, -2, -2, -1, -2, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 12776584
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -2, -2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, -1, -1, 1, -2, 1, 1, 1, -2, -1, 2, 2, 1, 1, 1, 2, 1, -2, 1, -1, 1, 1, 1, -2, -2, -1, -2, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 12776585
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, -2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12776586
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 0, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, -1, 2, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776541
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, 0, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776542
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 0, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 2, 2, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776543
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 0, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776544
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -2, -2, 0, 0, 0, 0, -2, -2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, -2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -2, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776545
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 0, -2, -1, -1, 1, 1, 1, -2, 2, -1, 1, 1, 1, 2, 2, 1, -2, 1, 1, -2, 1, -1, -1, 2, 1, 1, -2, -1, 1, -2, -2, -1, 1, 1, 1, 1, 1, 2, 1, -1, -1, -1, 2, -2, -2, 1, -2, 1, -1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776546
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, 0, -2, -1, -1, 1, 1, 1, -2, 2, -1, 1, 1, 1, 2, 2, 1, 1, 1, -2, 1, 1, 2, 2, -1, -2, -2, 1, -1, 1, 1, 1, 2, 1, -2, 1, -2, 1, -1, -2, -1, -1, -1, -1, -2, 1, 1, -2, 1, -1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776547
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 0, -2, -1, -1, 1, 1, 1, -2, 2, -1, 1, 1, 1, 2, 2, 1, 1, -2, 1, 1, -2, -1, -1, -1, 1, 1, 1, 2, 1, 1, 1, -1, 1, 1, 1, 1, -2, -1, 1, -1, 2, -1, -1, -2, 1, -2, -2, -2, 2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776548
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, 0, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, 0, -2, 2, 2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, -2, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -2, 1, 1, -1, -2, 1, -2, 1, 1, -1, 1, 2, -1, 2, -1, -2, 1, 1, -2, 1, -1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776549
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2j', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 0, -2, -2, -2, 4, -2, -2, -2, 1, 1, -2, 1, -2, 4, -2, 1, 1, 1, 0, 4, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, 1, -2, 1, -2, 1, -2, -2, 4, -2, -2, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, 4, -2, 1, 4, 1, 1, 1, 1, -2, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776550
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2k', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 0, -2, -2, -2, 4, -2, -2, -2, 1, 1, 1, -2, 4, -2, 1, 1, 1, -2, 0, 4, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, 1, 4, 1, 1, -2, -2, 1, -2, 4, 1, 1, -2, -2, 1, 4, -2, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, -2, -2, -2, 1, -2, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776552
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2l', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 0, -2, -2, -2, 4, -2, -2, 4, -2, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 4, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, 1, -2, -2, 1, 1, 4, 1, -2, -2, 1, 1, 1, 4, 1, -2, 1, 1, 1, 1, 1, -2, 4, 1, -2, 1, -2, 1, 1, -2, 1, -2, -2, -2, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776553
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2m', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 0, 4, 4, 4, 4, -2, -2, -2, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, -2, -2, 1, 1, 1, -2, 1, -2, -2, 1, 1, 1, -2, -2, -2, 1, 1, -2, 1, -2, -2, -2, 1, -2, -2, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776554
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2n', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, 4, 4, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, 4, 0, 0, 2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 2, 2, -4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 2, 2, 2, -4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776555
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2o', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, 4, 4, -2, -2, -2, 4, -2, -2, 4, 4, -2, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, -4, -4, 2, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776556
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2p', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, 4, -2, 0, 0, 2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, -4, 2, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776557
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2q', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, 4, 4, -2, -2, 4, -2, -2, -2, -2, -2, 4, -2, -2, 0, 0, -4, -4, 0, 0, 0, 0, -4, -4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -4, 2, -4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776558
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2r', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, -2, -2, 4, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, 0, 0, -4, -4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, -4, -4, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776559
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2s', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, 0, -2, -2, -2, 4, -2, -2, -2, 1, 1, -2, 1, -2, 4, -2, 1, 1, 1, 0, -4, -2, -2, 2, 2, 2, -4, 4, -2, 2, 2, 2, -2, -2, -1, 2, -1, 2, -1, 2, -2, 4, -2, 2, 2, -1, -2, -1, 2, -1, -2, -1, 2, -1, -4, 2, 1, -4, 1, 1, 1, 1, 2, -1, -1, 2, -1, 1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776560
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2t', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, 0, -2, -2, -2, 4, -2, -2, -2, 1, 1, 1, -2, 4, -2, 1, 1, 1, -2, 0, -4, -2, -2, 2, 2, 2, -4, 4, -2, 2, 2, 2, -2, -2, -1, -4, -1, -1, 2, 2, 1, -2, 4, -1, -1, 2, -2, -1, -4, 2, 1, -1, -1, -1, 2, 2, -2, 2, 1, 1, 1, -2, 2, 2, -1, 2, -1, 1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776561
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2u', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, 0, -2, -2, -2, 4, -2, -2, 4, -2, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, -4, -2, -2, 2, 2, 2, -4, 4, -2, 2, 2, 2, -2, -2, -1, 2, 2, -1, -1, -4, 1, -2, -2, -1, -1, -1, 4, -1, 2, -1, 1, -1, -1, -1, 2, -4, 1, 2, 1, -2, 1, 1, 2, -1, 2, 2, 2, -2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776563
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2v', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, 0, 4, 4, 4, 4, -2, -2, -2, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 0, -4, 4, 4, -4, -4, -4, -4, 4, 4, -4, -4, -4, -2, -2, 2, 2, -1, -1, -1, 2, 1, -2, -2, -1, -1, -1, -2, 2, 2, -1, 1, 2, -1, 2, 2, 2, 1, 2, -2, 1, -2, 1, 2, -1, -1, 2, -1, 1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776564
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2w', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, -2, -2, -2, 1, 1, -2, 1, -2, 4, -2, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 2, 2, -3, 0, 3, 0, 3, 0, 2, -4, 2, 0, 0, 3, 2, 3, 0, -3, 2, -3, 0, 3, 0, 0, -1, 0, -1, -1, -1, -1, 0, -3, 3, 0, -3, -1, -3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776565
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2x', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, -2, -2, -2, 1, 1, -2, 1, -2, 4, -2, 1, 1, 1, 0, 0, 2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 2, 2, 3, 0, -3, 0, -3, 0, 2, -4, 2, 0, 0, -3, 2, -3, 0, 3, 2, 3, 0, -3, 0, 0, -1, 0, -1, -1, -1, -1, 0, 3, -3, 0, 3, -1, 3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776566
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2y', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, -2, -2, -2, 1, 1, 1, -2, 4, -2, 1, 1, 1, -2, 0, 0, 2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 2, 2, -3, 0, -3, -3, 0, 0, -1, 2, -4, -3, 3, 0, 2, 3, 0, 0, -1, -3, 3, 3, 0, 0, 2, 0, -1, -1, -1, 2, 0, 0, -3, 0, 3, -1, 3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776567
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2z', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, -2, -2, -2, 1, 1, 1, -2, 4, -2, 1, 1, 1, -2, 0, 0, 2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 2, 2, 3, 0, 3, 3, 0, 0, -1, 2, -4, 3, -3, 0, 2, -3, 0, 0, -1, 3, -3, -3, 0, 0, 2, 0, -1, -1, -1, 2, 0, 0, 3, 0, -3, -1, -3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776568
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2aa', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, -2, -2, 4, -2, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, 2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 2, 2, -3, 0, 0, 3, -3, 0, -1, 2, 2, 3, -3, -3, -4, 3, 0, 3, -1, -3, -3, 3, 0, 0, -1, 0, -1, 2, -1, -1, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776569
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2ab', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 0, -2, -2, -2, 4, -2, -2, 4, -2, 1, 1, 1, -2, -2, 1, 1, -2, 1, 0, 0, 2, 2, 0, 0, 0, 0, -4, 2, 0, 0, 0, 2, 2, 3, 0, 0, -3, 3, 0, -1, 2, 2, -3, 3, 3, -4, -3, 0, -3, -1, 3, 3, -3, 0, 0, -1, 0, -1, 2, -1, -1, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776570
    {'cdim': 2, 'counter': 37, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2ac', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, -2, -2, -2, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 0, 0, -4, -4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 2, 2, 0, 0, -3, 3, 3, 0, -1, 2, 2, 3, -3, 3, 2, 0, 0, -3, -1, 0, -3, 0, 0, 0, -1, 0, 2, -1, 2, -1, 0, -3, -3, 0, 3, -1, 3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776571
    {'cdim': 2, 'counter': 38, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.2ad', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, -2, -2, -2, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 0, 0, -4, -4, 0, 0, 0, 0, -4, -4, 0, 0, 0, 2, 2, 0, 0, 3, -3, -3, 0, -1, 2, 2, -3, 3, -3, 2, 0, 0, 3, -1, 0, 3, 0, 0, 0, -1, 0, 2, -1, 2, -1, 0, 3, 3, 0, -3, -1, -3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776572
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.6a', 'multiplicity': 1, 'nt': [9, 11], 'qdim': 6, 'qvalues': [6, 6, 6, 0, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, -3, -3, 6, -3, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776574
    {'cdim': 6, 'counter': 40, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.6b', 'multiplicity': 1, 'nt': [9, 11], 'qdim': 6, 'qvalues': [6, 6, 6, 0, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 6, -3, 6, -3, -3, -3, -3, 6, -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, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776575
    {'cdim': 6, 'counter': 41, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.6c', 'multiplicity': 1, 'nt': [9, 11], 'qdim': 6, 'qvalues': [6, 6, 6, 0, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 6, -3, 6, -3, 6, -3, -3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776576
    {'cdim': 6, 'counter': 42, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.6d', 'multiplicity': 1, 'nt': [18, 41], 'qdim': 6, 'qvalues': [6, 6, -6, 0, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3, 3, 3, 3, 3, -3, 6, 3, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776577
    {'cdim': 6, 'counter': 43, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.6e', 'multiplicity': 1, 'nt': [18, 41], 'qdim': 6, 'qvalues': [6, 6, -6, 0, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, 6, 3, -6, 3, 3, -3, -3, -6, 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, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776578
    {'cdim': 6, 'counter': 44, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.6f', 'multiplicity': 1, 'nt': [18, 41], 'qdim': 6, 'qvalues': [6, 6, -6, 0, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 6, -3, -6, 3, -6, 3, -3, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776579
    {'cdim': 6, 'counter': 45, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.6g', 'multiplicity': 2, 'nt': [36, 190], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -6, -6, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 6, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12776580
    {'cdim': 6, 'counter': 46, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.6h', 'multiplicity': 2, 'nt': [36, 190], 'qdim': 12, 'qvalues': [12, -12, 0, 0, -6, 12, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -12, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12776581
    {'cdim': 6, 'counter': 47, 'faithful': False, 'group': '648.496', 'group_order': 648, 'image': None, 'label': '648.496.6i', 'multiplicity': 2, 'nt': [36, 190], 'qdim': 12, 'qvalues': [12, -12, 0, 0, 12, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 6, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 29533429
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  • id: 29533440
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 324, 'label': '648.496.1b', '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]]]}
  • id: 29533451
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 324, 'label': '648.496.1c', '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]]]}
  • id: 29533462
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 324, 'label': '648.496.1d', '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]]]}
  • id: 29533473
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  • id: 29533484
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 216, 'label': '648.496.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[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, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 29533495
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 108, 'label': '648.496.1f1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[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, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 29533502
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1', 'kernel_order': 108, 'label': '648.496.1f2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[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, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 29533503
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 108, 'label': '648.496.1g1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[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, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 29533430
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.d1', 'kernel_order': 108, 'label': '648.496.1g2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[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, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 29533431
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 108, 'label': '648.496.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[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, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 29533432
    {'center': '1.a1', 'center_index': 1, 'center_order': 648, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1', 'kernel_order': 108, 'label': '648.496.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[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, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 29533433
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.c1', 'kernel_order': 108, 'label': '648.496.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533480
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 56, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2aa1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 1]], [[-2, -1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 1]], [[1, 0], [2, 1]], [[1, -1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533481
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 57, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2aa2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-2, 0]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, -1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, -1]], [[-1, 0], [-2, 1]], [[1, 1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533482
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 58, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2ab1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-2, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 1]], [[-1, 0], [-2, 1]], [[1, -1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533483
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 59, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2ab2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, -1]], [[-2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[-2, 0]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, -1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, -1]], [[1, 0], [2, 1]], [[1, 1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533485
    {'center': '12.a1', 'center_index': 12, 'center_order': 54, 'counter': 60, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.496.2ac1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 1]], [[1, 0], [2, 1]], [[-2, -1]], [[1, -1]], [[-2, 1]], [[1, -1]], [[0, 0]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533486
    {'center': '12.a1', 'center_index': 12, 'center_order': 54, 'counter': 61, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.496.2ac2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[1, -1]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, -1]], [[-1, 0], [-2, 1]], [[-2, 1]], [[1, 1]], [[-2, -1]], [[1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, -1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533487
    {'center': '12.a1', 'center_index': 12, 'center_order': 54, 'counter': 62, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.496.2ad1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 1]], [[-1, 0], [-2, 1]], [[-2, -1]], [[1, -1]], [[-2, 1]], [[1, -1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533488
    {'center': '12.a1', 'center_index': 12, 'center_order': 54, 'counter': 63, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1', 'kernel_order': 9, 'label': '648.496.2ad2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, -1]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, -1]], [[1, 0], [2, 1]], [[-2, 1]], [[1, 1]], [[-2, -1]], [[1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, -1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533434
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.c1', 'kernel_order': 108, 'label': '648.496.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533435
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.c1', 'kernel_order': 108, 'label': '648.496.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533436
    {'center': '6.a1', 'center_index': 6, 'center_order': 108, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 108, 'label': '648.496.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533437
    {'center': '4.a1', 'center_index': 4, 'center_order': 162, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.a1', 'kernel_order': 81, 'label': '648.496.2e', 'nt': [4, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533438
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 54, 'label': '648.496.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533439
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 54, 'label': '648.496.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533441
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1', 'kernel_order': 54, 'label': '648.496.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533442
    {'center': '6.a1', 'center_index': 6, 'center_order': 108, 'counter': 21, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 54, 'label': '648.496.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[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]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533443
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 22, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 36, 'label': '648.496.2j1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533444
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 23, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 36, 'label': '648.496.2j2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533445
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 24, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 36, 'label': '648.496.2k1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533446
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 25, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 36, 'label': '648.496.2k2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533447
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 26, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 36, 'label': '648.496.2l1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533448
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 27, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 36, 'label': '648.496.2l2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533449
    {'center': '6.a1', 'center_index': 6, 'center_order': 108, 'counter': 28, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1', 'kernel_order': 36, 'label': '648.496.2m1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[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, 1]], [[2, -1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533450
    {'center': '6.a1', 'center_index': 6, 'center_order': 108, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1', 'kernel_order': 36, 'label': '648.496.2m2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[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, -1]], [[2, 1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533452
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 27, 'label': '648.496.2n1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533453
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 27, 'label': '648.496.2n2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533454
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 27, 'label': '648.496.2o1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533455
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 33, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 27, 'label': '648.496.2o2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533456
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 34, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 27, 'label': '648.496.2p1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533457
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 35, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1', 'kernel_order': 27, 'label': '648.496.2p2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533458
    {'center': '12.a1', 'center_index': 12, 'center_order': 54, 'counter': 36, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 27, 'label': '648.496.2q1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533459
    {'center': '12.a1', 'center_index': 12, 'center_order': 54, 'counter': 37, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 27, 'label': '648.496.2q2', 'nt': [12, 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]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533460
    {'center': '4.a1', 'center_index': 4, 'center_order': 162, 'counter': 38, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1', 'kernel_order': 27, 'label': '648.496.2r1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533461
    {'center': '4.a1', 'center_index': 4, 'center_order': 162, 'counter': 39, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1', 'kernel_order': 27, 'label': '648.496.2r2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533463
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 40, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 18, 'label': '648.496.2s1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 1]], [[2, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-2, 1]], [[1, 1]], [[1, 0]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-2, -1]], [[-2, -1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[2, 1]], [[1, 1]], [[-2, 1]], [[1, -1]], [[-2, 0]], [[1, 0]], [[-1, 1]], [[-2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-2, 1]], [[1, -1]], [[1, -1]], [[-2, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533464
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 41, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 18, 'label': '648.496.2s2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, -1]], [[2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-2, -1]], [[1, -1]], [[1, 0]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-2, 1]], [[-2, 1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[2, -1]], [[1, -1]], [[-2, -1]], [[1, 1]], [[-2, 0]], [[1, 0]], [[-1, -1]], [[-2, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-2, -1]], [[1, 1]], [[1, 1]], [[-2, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533465
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 42, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 18, 'label': '648.496.2t1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 1]], [[2, -1]], [[1, -1]], [[-2, 0]], [[1, 1]], [[1, 1]], [[-2, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[1, -1]], [[1, -1]], [[-2, -1]], [[-1, 0]], [[1, 1]], [[-2, 0]], [[-2, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[2, 1]], [[1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[-2, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533466
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 43, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 18, 'label': '648.496.2t2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, -1]], [[2, 1]], [[1, 1]], [[-2, 0]], [[1, -1]], [[1, -1]], [[-2, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[1, 1]], [[1, 1]], [[-2, 1]], [[-1, 0]], [[1, -1]], [[-2, 0]], [[-2, -1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[2, -1]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[-2, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533467
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 44, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 18, 'label': '648.496.2u1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 1]], [[2, -1]], [[1, -1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[1, 1]], [[-2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[2, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, 0]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-2, 1]], [[1, -1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533468
    {'center': '6.c1', 'center_index': 6, 'center_order': 108, 'counter': 45, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 18, 'label': '648.496.2u2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, -1]], [[2, 1]], [[1, 1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[1, -1]], [[-2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[2, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 0]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-2, -1]], [[1, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533469
    {'center': '6.a1', 'center_index': 6, 'center_order': 108, 'counter': 46, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 18, 'label': '648.496.2v1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[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, 1]], [[2, -1]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[-2, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-2, 1]], [[1, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 0]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[-2, 1]], [[1, -1]], [[1, -1]], [[-2, -1]], [[1, -1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533470
    {'center': '6.a1', 'center_index': 6, 'center_order': 108, 'counter': 47, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 18, 'label': '648.496.2v2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[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, -1]], [[2, 1]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-2, -1]], [[1, 0]], [[1, -1]], [[-1, -1]], [[-2, -1]], [[1, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[1, 0]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[-2, -1]], [[1, 1]], [[1, 1]], [[-2, 1]], [[1, 1]], [[-1, -1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533471
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 48, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2w1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 1]], [[-2, -1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, -1]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 1]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533472
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 49, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2w2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 1]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, -1]], [[-1, 0], [1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, -1]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, -1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533474
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 50, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2x1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-2, -1]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-2, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 1]], [[0, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533475
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 51, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2x2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, -1]], [[-2, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 1]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, 0]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-2, -1]], [[1, 0], [-1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, -1]], [[0, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, -1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533476
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 52, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2y1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 1]], [[-2, -1]], [[-1, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, -1]], [[1, 0]], [[-2, 0]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-2, 1]], [[-1, 0], [-2, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533477
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 53, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2y2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 1]], [[1, 0]], [[-2, 0]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-2, -1]], [[1, 0], [2, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, -1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533478
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 54, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2z1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, -1]], [[1, 0]], [[-2, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[-2, 1]], [[1, 0], [2, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533479
    {'center': '12.c1', 'center_index': 12, 'center_order': 54, 'counter': 55, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.c1', 'kernel_order': 9, 'label': '648.496.2z2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, -1]], [[-2, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 1]], [[1, 0]], [[-2, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-2, -1]], [[-1, 0], [-2, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, -1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533489
    {'center': '54.a1', 'center_index': 54, 'center_order': 12, 'counter': 64, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '54.5', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 12, 'label': '648.496.6a', 'nt': [9, 11], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29533490
    {'center': '54.a1', 'center_index': 54, 'center_order': 12, 'counter': 65, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '54.5', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 12, 'label': '648.496.6b', 'nt': [9, 11], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29533491
    {'center': '54.a1', 'center_index': 54, 'center_order': 12, 'counter': 66, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '54.5', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 12, 'label': '648.496.6c', 'nt': [9, 11], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29533492
    {'center': '54.a1', 'center_index': 54, 'center_order': 12, 'counter': 67, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '108.25', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 6, 'label': '648.496.6d', 'nt': [18, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[6, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29533493
    {'center': '54.a1', 'center_index': 54, 'center_order': 12, 'counter': 68, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '108.25', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 6, 'label': '648.496.6e', 'nt': [18, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29533494
    {'center': '54.a1', 'center_index': 54, 'center_order': 12, 'counter': 69, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '108.25', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 6, 'label': '648.496.6f', 'nt': [18, 41], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[6, 0]], [[-3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 29533496
    {'center': '108.a1', 'center_index': 108, 'center_order': 6, 'counter': 70, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '216.60', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 3, 'label': '648.496.6g1', 'nt': [36, 190], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [-6, 1]], [[3, 0]], [[3, 0]], [[-3, 0], [-6, 1]], [[3, 0], [6, 1]], [[3, 0], [6, 1]], [[3, 0], [6, 1]], [[3, 0]], [[-6, 0]], [[-3, 0], [-6, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533497
    {'center': '108.a1', 'center_index': 108, 'center_order': 6, 'counter': 71, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '216.60', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 3, 'label': '648.496.6g2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [6, 1]], [[3, 0]], [[3, 0]], [[3, 0], [6, 1]], [[-3, 0], [-6, 1]], [[-3, 0], [-6, 1]], [[-3, 0], [-6, 1]], [[3, 0]], [[-6, 0]], [[3, 0], [6, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533498
    {'center': '108.a1', 'center_index': 108, 'center_order': 6, 'counter': 72, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '216.60', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 3, 'label': '648.496.6h1', 'nt': [36, 190], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [-6, 1]], [[3, 0]], [[-6, 0]], [[3, 0], [6, 1]], [[0, 0]], [[-3, 0], [-6, 1]], [[3, 0], [6, 1]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 0], [6, 1]], [[-3, 0], [-6, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533499
    {'center': '108.a1', 'center_index': 108, 'center_order': 6, 'counter': 73, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '216.60', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 3, 'label': '648.496.6h2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [6, 1]], [[3, 0]], [[-6, 0]], [[-3, 0], [-6, 1]], [[0, 0]], [[3, 0], [6, 1]], [[-3, 0], [-6, 1]], [[3, 0]], [[3, 0]], [[0, 0]], [[-3, 0], [-6, 1]], [[3, 0], [6, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533500
    {'center': '108.a1', 'center_index': 108, 'center_order': 6, 'counter': 74, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '216.60', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 3, 'label': '648.496.6i1', 'nt': [36, 190], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0], [-6, 1]], [[-6, 0]], [[3, 0]], [[0, 0]], [[-3, 0], [-6, 1]], [[0, 0]], [[3, 0], [6, 1]], [[3, 0]], [[3, 0]], [[3, 0], [6, 1]], [[-3, 0], [-6, 1]], [[3, 0], [6, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 29533501
    {'center': '108.a1', 'center_index': 108, 'center_order': 6, 'counter': 75, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '648.496', 'group_counter': 496, 'group_order': 648, 'image': None, 'image_isoclass': '216.60', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 3, 'label': '648.496.6i2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0], [6, 1]], [[-6, 0]], [[3, 0]], [[0, 0]], [[3, 0], [6, 1]], [[0, 0]], [[-3, 0], [-6, 1]], [[3, 0]], [[3, 0]], [[-3, 0], [-6, 1]], [[3, 0], [6, 1]], [[-3, 0], [-6, 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]], [[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: 110386560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 648, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '648.496.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.496', 'subgroup_hash': 496, 'subgroup_order': 648, 'subgroup_tex': '(C_3\\times C_6^2):C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386612
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 324, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.152', 'subgroup_hash': 152, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 110386634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.98', 'subgroup_hash': 98, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110386645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 216, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, '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': '216.149', 'subgroup_hash': 149, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 110386656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.3.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.144', 'subgroup_hash': 144, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.3.c1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.60', 'subgroup_hash': 60, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 162, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': 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: 110386689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 81, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': 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: 110386561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': 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: 110386572
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, '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': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 110386605
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 108, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1', 'outer_equivalence': True, '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': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386607
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 108, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1', 'outer_equivalence': True, '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': '108.34', 'subgroup_hash': 34, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386608
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 36, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386609
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 110386610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.6.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.6.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.6.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110386614
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.6.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110386615
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 81, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '648.496.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 110386616
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110386617
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110386618
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 12, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.9.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110386619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.9.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110386620
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.9.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110386621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 54, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': 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: 110386622
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 54, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, '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': ['D', 'L1', 'D1'], '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: 110386624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 110386625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386626
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386633
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.12.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386636
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 36, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, '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': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386638
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 36, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386639
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386640
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386641
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386642
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386643
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386647
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386648
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386649
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386650
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386653
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110386654
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.18.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386655
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 27, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 110386657
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 27, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 110386658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 110386659
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386663
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.27.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386665
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 18, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, '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': ['S', 'C4'], '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: 110386666
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 18, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:S_3', 'simple': False, 'solvable': True, 'special_labels': [], '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: 110386668
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.c1', 'outer_equivalence': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386669
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386670
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386671
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386672
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386673
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386674
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386675
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386676
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386677
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 9, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386679
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386680
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386681
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386682
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386685
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386686
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386687
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.36.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386688
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 12, 'counter': 89, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.5', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 110386690
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 12, 'counter': 90, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 110386691
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386692
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386693
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386694
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386695
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386696
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386697
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386699
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386562
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386563
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.54.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 110386564
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.54.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386565
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 9, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], '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: 110386566
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 9, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.35', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386567
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386574
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '648.496.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 2}
  • id: 110386575
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 112, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.496.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.25', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, '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': ['C5'], '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: 110386576
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 6, 'counter': 113, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.496.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.43', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, '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': ['Phi'], '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: 110386577
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386578
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386579
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386580
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 117, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386581
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 118, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386582
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 119, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386585
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386586
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 110386587
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386588
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386589
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386590
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386591
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': 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: 110386592
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '648.496.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '162.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:C_6', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386593
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '648.496.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 110386595
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 110386596
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 131, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.496.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.60', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 60, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:C_6', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 110386597
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 3, 'counter': 132, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.496.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.144', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 144, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:C_6', 'simple': True, 'solvable': True, 'special_labels': [], '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: 110386598
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110386599
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 134, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110386600
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110386601
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110386602
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 2, 'counter': 137, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '648.496.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.144', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 144, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:D_6', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 110386603
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 138, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110386604
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 139, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '648.496.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 110386606
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '648.496', 'ambient_counter': 496, 'ambient_order': 648, 'ambient_tex': '(C_3\\times C_6^2):C_6', 'central': True, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 1, 'counter': 140, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '648.496.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '648.496', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 496, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_3\\times C_6^2):C_6', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 110386560
    {'ambient': '648.496', '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': '324.a1', 'complements': ['648.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '3.a1', '3.b1', '3.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6559, 3445, 6500, 3101], 'generators': [3, 36, 42, 54, 216, 2, 324], 'label': '648.496.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '324.144'}
  • id: 110386561
    {'ambient': '648.496', 'aut_centralizer_order': 2, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '5832.et', 'aut_weyl_index': 4, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1'], 'contains': ['8.a1', '12.k1', '12.l1', '12.m1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7822, -1, 9351, -1], 'generators': [3, 216, 2, 42, 36], 'label': '648.496.4.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '4.c1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '162.40'}
  • id: 110386562
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1', '18.q1', '18.r1', '27.c1'], 'contains': ['108.b1', '162.c1'], 'core': '108.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6705, -1, 6899, -1], 'generators': [417, 324, 36], 'label': '648.496.54.l1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.l1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386563
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '54.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1', '18.q1', '27.a1'], 'contains': ['108.c1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5366, -1, 7081, -1], 'generators': [93, 2, 324], 'label': '648.496.54.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.m1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386564
    {'ambient': '648.496', 'aut_centralizer_order': 24, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.o1', '18.r1', '27.d1'], 'contains': ['108.d1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9119, -1, 7448, -1], 'generators': [417, 324, 78], 'label': '648.496.54.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.n1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386565
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '72.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.b1', '24.d1', '36.a1', '36.l1', '36.t1'], 'contains': ['216.a1', '216.b1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3665, 3977, 3925, 4663], 'generators': [36, 216], 'label': '648.496.72.a1', 'mobius_quo': 3, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['24.a1', '24.b1', '36.a1'], 'normal_contains': ['216.a1', '216.b1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '648.496', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.14', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386566
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '72.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.a1', 'complements': ['9.c1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.c1', '36.b1', '36.m1', '36.r1'], 'contains': ['216.b1', '216.c1'], 'core': '72.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4389, 3169, 4256, 3882], 'generators': [2, 36], 'label': '648.496.72.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': ['24.a1', '24.c1', '36.b1'], 'normal_contains': ['216.b1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '648.496', 'quotient_action_image': '6.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386567
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '72.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.b1', 'complements': ['9.a1'], 'conjugacy_class_count': 3, 'contained_in': ['24.b1', '24.c1', '24.e1', '36.c1', '36.n1', '36.u1'], 'contains': ['216.b1', '216.d1'], 'core': '72.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4995, 1555, 4090, 3092], 'generators': [42, 36], 'label': '648.496.72.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.c1', 'normal_contained_in': ['24.b1', '24.c1', '36.c1'], 'normal_contains': ['216.b1'], 'normalizer': '1.a1', 'old_label': '72.c1', 'projective_image': '648.496', 'quotient_action_image': '6.2', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110386568
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '36.d1', '36.i1', '36.q1'], 'contains': ['216.a1', '216.c1', '216.e1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3428, -1, 5168, -1], 'generators': [2, 252], 'label': '648.496.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '72.d1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386569
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.b1', '36.e1', '36.j1', '36.s1'], 'contains': ['216.a1', '216.d1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6868, -1, 5333, -1], 'generators': [42, 252], 'label': '648.496.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '72.e1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386570
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.d1', '36.f1', '36.k1'], 'contains': ['216.a1', '216.f1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [760, -1, 1130, -1], 'generators': [44, 252], 'label': '648.496.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '72.f1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386571
    {'ambient': '648.496', 'aut_centralizer_order': 972, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '24.e1', '36.g1', '36.o1'], 'contains': ['216.b1', '216.e1'], 'core': '216.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2215, -1, 3263, -1], 'generators': [218, 36], 'label': '648.496.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.g1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386572
    {'ambient': '648.496', 'aut_centralizer_order': 162, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 162, 'centralizer': '6.a1', 'complements': ['108.p1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '12.f1', '18.a1', '18.b1', '18.d1', '18.g1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3685, 9193, 4528, 9143], 'generators': [54, 216, 324, 2, 36], 'label': '648.496.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.a1', '18.a1', '18.b1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '324.144', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386573
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['24.c1', '24.d1', '24.e1', '36.h1', '36.p1'], 'contains': ['216.b1', '216.f1'], 'core': '216.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1578, -1, 1441, -1], 'generators': [44, 36], 'label': '648.496.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.h1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386574
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.b1', '27.c1', '27.d1'], 'contains': ['162.a1', '162.b1', '162.c1'], 'core': '162.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8239, -1, 7614, -1], 'generators': [3, 54], 'label': '648.496.81.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '81.a1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110386575
    {'ambient': '648.496', 'aut_centralizer_order': 3888, 'aut_label': '108.a1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['36.a1', '36.d1', '36.e1', '36.f1', '54.a1', '54.h1', '54.k1'], 'contains': ['216.a1', '324.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5695, 6290, 5489, 6584], 'generators': [324, 252], 'label': '648.496.108.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': ['36.a1', '54.a1'], 'normal_contains': ['216.a1', '324.a1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.10', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386576
    {'ambient': '648.496', 'aut_centralizer_order': 11664, 'aut_label': '108.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.b1', '36.c1', '36.g1', '36.h1', '54.b1', '54.i1', '54.l1'], 'contains': ['216.b1', '324.a1'], 'core': '108.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5401, 5453, 5013, 5755], 'generators': [324, 36], 'label': '648.496.108.b1', 'mobius_quo': 1, 'mobius_sub': -54, 'normal_closure': '108.b1', 'normal_contained_in': ['36.a1', '36.b1', '36.c1', '54.b1'], 'normal_contains': ['216.b1', '324.a1'], 'normalizer': '1.a1', 'old_label': '108.b1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.15', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386577
    {'ambient': '648.496', 'aut_centralizer_order': 3888, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.d1', '54.c1', '54.g1', '54.m1'], 'contains': ['216.c1', '324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5178, -1, 5846, -1], 'generators': [324, 2], 'label': '648.496.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.c1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386578
    {'ambient': '648.496', 'aut_centralizer_order': 1296, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.c1', '36.e1', '54.d1', '54.j1', '54.n1'], 'contains': ['216.d1', '324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7463, -1, 6121, -1], 'generators': [324, 78], 'label': '648.496.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.d1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386579
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1', '36.g1', '54.e1'], 'contains': ['216.e1', '324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2574, -1, 4702, -1], 'generators': [324, 218], 'label': '648.496.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '108.e1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386580
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.f1', '36.h1', '54.f1'], 'contains': ['216.f1', '324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [864, -1, 1285, -1], 'generators': [324, 44], 'label': '648.496.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '108.f1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386581
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.i1', '36.j1', '36.k1', '36.l1', '54.a1'], 'contains': ['216.a1', '324.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2433, -1, 3770, -1], 'generators': [54, 252], 'label': '648.496.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '108.g1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386582
    {'ambient': '648.496', 'aut_centralizer_order': 5832, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.m1', '36.n1', '36.o1', '36.p1', '54.b1'], 'contains': ['216.b1', '324.b1'], 'core': '216.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2948, -1, 2561, -1], 'generators': [54, 36], 'label': '648.496.108.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '108.h1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386583
    {'ambient': '648.496', 'aut_centralizer_order': 54, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.545', 'aut_weyl_index': 54, 'centralizer': '6.b1', 'complements': ['108.m1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.b1', '12.g1', '18.a1', '18.c1', '18.e1'], 'core': '6.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5756, 5532, 4845, 5642], 'generators': [54, 216, 324, 42, 36], 'label': '648.496.6.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1', 'normal_contained_in': ['2.a1', '3.a1'], 'normal_contains': ['12.b1', '18.a1', '18.c1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '324.144', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110386584
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1', '36.m1', '54.c1'], 'contains': ['216.c1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3326, -1, 4411, -1], 'generators': [54, 2], 'label': '648.496.108.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '108.i1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386585
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.j1', '36.n1', '54.d1'], 'contains': ['216.d1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6243, -1, 4557, -1], 'generators': [54, 78], 'label': '648.496.108.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '108.j1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386586
    {'ambient': '648.496', 'aut_centralizer_order': 972, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.i1', '36.o1', '54.e1'], 'contains': ['216.e1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1690, -1, 3624, -1], 'generators': [54, 218], 'label': '648.496.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '108.k1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386587
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['36.k1', '36.p1', '54.f1'], 'contains': ['216.f1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [577, -1, 942, -1], 'generators': [54, 44], 'label': '648.496.108.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '108.l1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386588
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '36.r1', '54.g1'], 'contains': ['216.c1', '324.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6685, -1, 8288, -1], 'generators': [3, 2], 'label': '648.496.108.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '108.m1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386589
    {'ambient': '648.496', 'aut_centralizer_order': 72, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.q1', '36.s1', '36.t1', '54.h1'], 'contains': ['216.a1', '324.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8518, -1, 8578, -1], 'generators': [3, 252], 'label': '648.496.108.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '108.n1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386590
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1', '36.t1', '36.u1', '54.i1'], 'contains': ['216.b1', '324.c1'], 'core': '216.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [9049, -1, 8433, -1], 'generators': [3, 36], 'label': '648.496.108.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '108.o1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386591
    {'ambient': '648.496', 'aut_centralizer_order': 24, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.s1', '36.u1', '54.j1'], 'contains': ['216.d1', '324.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [9504, -1, 8724, -1], 'generators': [3, 78], 'label': '648.496.108.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.j1', 'old_label': '108.p1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386592
    {'ambient': '648.496', 'aut_centralizer_order': 11664, 'aut_label': '162.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '2.a1', 'complements': ['4.c1'], 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.b1', '54.c1', '54.d1', '54.e1', '54.f1', '81.a1'], 'contains': ['324.a1', '324.b1'], 'core': '162.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3823, 7185, 4857, 8165], 'generators': [54, 324], 'label': '648.496.162.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '162.a1', 'normal_contained_in': ['54.a1', '54.b1'], 'normal_contains': ['324.a1'], 'normalizer': '1.a1', 'old_label': '162.a1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '81.12', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386593
    {'ambient': '648.496', 'aut_centralizer_order': 432, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.g1', '54.h1', '54.i1', '54.j1', '81.a1'], 'contains': ['324.a1', '324.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8336, -1, 8034, -1], 'generators': [3, 324], 'label': '648.496.162.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.b1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386594
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 324, 'centralizer': '18.a1', 'complements': ['108.n1', '108.p1'], 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '3.c1'], 'contains': ['12.c1', '12.i1', '18.b1', '18.c1', '18.h1'], 'core': '6.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5061, 7363, 3764, 7393], 'generators': [54, 36, 324, 2, 42], 'label': '648.496.6.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.c1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.c1', '18.b1', '18.c1'], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 110386595
    {'ambient': '648.496', 'aut_centralizer_order': 432, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '54.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.k1', '54.l1', '54.m1', '54.n1', '81.a1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7080, -1, 7172, -1], 'generators': [417], 'label': '648.496.162.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.c1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386596
    {'ambient': '648.496', 'aut_centralizer_order': 3888, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '2.a1', 'complements': ['3.c1'], 'conjugacy_class_count': 3, 'contained_in': ['72.a1', '72.d1', '72.e1', '72.f1', '108.a1', '108.g1', '108.n1'], 'contains': ['648.a1'], 'core': '216.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3540, 4981, 5023, 5407], 'generators': [252], 'label': '648.496.216.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': ['72.a1', '108.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '648.496', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.30', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386597
    {'ambient': '648.496', 'aut_centralizer_order': 11664, 'aut_label': '216.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.b1', '72.c1', '72.g1', '72.h1', '108.b1', '108.h1', '108.o1'], 'contains': ['648.a1'], 'core': '216.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3750, 3977, 4090, 4663], 'generators': [36], 'label': '648.496.216.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.b1', 'normal_contained_in': ['72.a1', '72.b1', '72.c1', '108.b1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '216.b1', 'projective_image': '648.496', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.45', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386598
    {'ambient': '648.496', 'aut_centralizer_order': 3888, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1', '72.d1', '108.c1', '108.i1', '108.m1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4044, -1, 5168, -1], 'generators': [2], 'label': '648.496.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '216.c1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386599
    {'ambient': '648.496', 'aut_centralizer_order': 1296, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.c1', '72.e1', '108.d1', '108.j1', '108.p1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6888, -1, 5323, -1], 'generators': [78], 'label': '648.496.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.d1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386600
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.g1', '108.e1', '108.k1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2330, -1, 4702, -1], 'generators': [218], 'label': '648.496.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '216.e1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386601
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.f1', '72.h1', '108.f1', '108.l1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [864, -1, 1285, -1], 'generators': [44], 'label': '648.496.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '216.f1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386602
    {'ambient': '648.496', 'aut_centralizer_order': 23328, 'aut_label': '324.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 23328, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.b1', '108.c1', '108.d1', '108.e1', '108.f1', '162.a1', '162.b1', '162.c1'], 'contains': ['648.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5364, 5994, 5485, 6113], 'generators': [324], 'label': '648.496.324.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '324.a1', 'normal_contained_in': ['108.a1', '108.b1', '162.a1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '324.a1', 'projective_image': '324.144', 'quotient_action_image': '1.1', 'quotient_action_kernel': '324.144', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386603
    {'ambient': '648.496', 'aut_centralizer_order': 11664, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 23328, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1', '108.h1', '108.i1', '108.j1', '108.k1', '108.l1', '162.a1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3072, -1, 3856, -1], 'generators': [54], 'label': '648.496.324.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '162.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '324.b1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386604
    {'ambient': '648.496', 'aut_centralizer_order': 432, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 23328, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.m1', '108.n1', '108.o1', '108.p1', '162.b1'], 'contains': ['648.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [8451, -1, 8361, -1], 'generators': [3], 'label': '648.496.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1', 'old_label': '324.c1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386605
    {'ambient': '648.496', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '324.a1', 'complements': ['108.i1', '108.k1', '108.l1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.b1', '12.m1', '18.k1', '18.l1', '18.m1'], 'core': '6.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [9026, 837, 8552, 2198], 'generators': [3, 216, 324, 42, 36], 'label': '648.496.6.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1', 'normal_contained_in': ['2.b1', '3.a1'], 'normal_contains': ['12.b1'], 'normalizer': '1.a1', 'old_label': '6.d1', 'projective_image': '324.144', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '324.144'}
  • id: 110386606
    {'ambient': '648.496', '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': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.b1', '216.c1', '216.d1', '216.e1', '216.f1', '324.a1', '324.b1', '324.c1'], 'contains': [], 'core': '648.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3750, 4981, 5023, 5407], 'generators': [], 'label': '648.496.648.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': ['216.a1', '216.b1', '324.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386607
    {'ambient': '648.496', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '324.a1', 'complements': ['108.i1', '108.k1', '108.l1', '108.m1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.b1', '18.o1', '18.p1', '18.r1'], 'core': '6.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [7264, 2322, 6102, 776], 'generators': [417, 216, 324, 42, 36], 'label': '648.496.6.e1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1', 'normal_contained_in': ['2.c1', '3.a1'], 'normal_contains': ['12.b1'], 'normalizer': '1.a1', 'old_label': '6.e1', 'projective_image': '324.144', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '324.144'}
  • id: 110386608
    {'ambient': '648.496', 'aut_centralizer_order': 54, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['12.d1', '12.h1', '18.a1', '18.f1', '18.h1'], 'core': '18.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1315, -1, 1009, -1], 'generators': [54, 216, 324, 44, 36], 'label': '648.496.6.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '6.f1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386609
    {'ambient': '648.496', 'aut_centralizer_order': 54, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 324, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1'], 'contains': ['12.e1', '12.j1', '18.c1', '18.g1', '18.h1'], 'core': '18.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [2248, -1, 2960, -1], 'generators': [54, 36, 324, 218, 42], 'label': '648.496.6.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '6.g1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 110386610
    {'ambient': '648.496', 'aut_centralizer_order': 18, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.545', 'aut_weyl_index': 54, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.a1', '12.k1', '18.i1', '18.j1', '18.l1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6933, -1, 8195, -1], 'generators': [3, 216, 324, 2, 36], 'label': '648.496.6.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.h1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 110386611
    {'ambient': '648.496', 'aut_centralizer_order': 12, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.b1', '3.c1'], 'contains': ['12.c1', '12.l1', '18.j1', '18.m1'], 'core': '12.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [7578, -1, 7801, -1], 'generators': [3, 36, 324, 2, 42], 'label': '648.496.6.i1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.i1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 110386612
    {'ambient': '648.496', 'aut_centralizer_order': 18, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1296.2985', 'aut_weyl_index': 18, 'centralizer': '18.a1', 'complements': ['324.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '6.a1', '6.b1', '6.c1', '6.f1', '6.g1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3870, 6280, 3969, 6151], 'generators': [54, 36, 216, 324, 2, 42], 'label': '648.496.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.a1', '6.b1', '6.c1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 110386613
    {'ambient': '648.496', 'aut_centralizer_order': 18, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.545', 'aut_weyl_index': 54, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.b1'], 'contains': ['12.a1', '18.n1', '18.p1', '18.q1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5435, -1, 5798, -1], 'generators': [93, 216, 2, 324, 36], 'label': '648.496.6.j1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.j1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 110386614
    {'ambient': '648.496', 'aut_centralizer_order': 12, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.c1', '3.c1'], 'contains': ['12.c1', '18.q1', '18.r1'], 'core': '12.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [6182, -1, 5463, -1], 'generators': [93, 36, 2, 324, 42], 'label': '648.496.6.k1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.k1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 110386615
    {'ambient': '648.496', 'aut_centralizer_order': 36, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '648.555', 'aut_weyl_index': 36, 'centralizer': '18.a1', 'complements': ['81.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['24.a1', '24.b1', '24.c1', '24.d1', '24.e1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4128, 1082, 2262, 1322], 'generators': [2, 42, 216], 'label': '648.496.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['24.a1', '24.b1', '24.c1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '648.496', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 110386616
    {'ambient': '648.496', 'aut_centralizer_order': 18, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.51', 'aut_weyl_index': 486, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.b1'], 'contains': ['18.d1', '18.i1', '18.n1', '27.a1', '27.b1'], 'core': '54.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5902, -1, 6722, -1], 'generators': [3, 252, 54, 2, 324], 'label': '648.496.9.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386617
    {'ambient': '648.496', 'aut_centralizer_order': 54, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 486, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1', '3.c1'], 'contains': ['18.b1', '18.j1', '18.q1', '27.a1', '27.c1'], 'core': '18.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6352, -1, 6385, -1], 'generators': [3, 36, 54, 2, 324], 'label': '648.496.9.b1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386618
    {'ambient': '648.496', 'aut_centralizer_order': 2, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '432.545', 'aut_weyl_index': 54, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.a1'], 'contains': ['18.e1', '18.k1', '18.o1', '27.b1', '27.d1'], 'core': '54.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8552, -1, 7460, -1], 'generators': [3, 252, 54, 324, 42], 'label': '648.496.9.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '9.c1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 110386619
    {'ambient': '648.496', 'aut_centralizer_order': 18, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.545', 'aut_weyl_index': 54, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.a1', '18.l1', '18.p1', '27.b1', '27.c1'], 'core': '18.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7993, -1, 7004, -1], 'generators': [3, 216, 54, 324, 36], 'label': '648.496.9.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '9.d1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 110386620
    {'ambient': '648.496', 'aut_centralizer_order': 6, 'aut_label': '9.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '432.545', 'aut_weyl_index': 54, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.a1', '3.c1'], 'contains': ['18.c1', '18.m1', '18.r1', '27.c1', '27.d1'], 'core': '18.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [8762, -1, 7232, -1], 'generators': [3, 36, 54, 324, 42], 'label': '648.496.9.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '9.e1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.e1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 110386621
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 324, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1', '6.h1', '6.j1'], 'contains': ['24.a1', '36.a1', '36.b1', '36.d1', '36.g1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3626, 5955, 4696, 6264], 'generators': [324, 2, 36, 216], 'label': '648.496.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['24.a1', '36.a1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '324.144', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386622
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '12.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '6.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.b1', '6.d1', '6.e1'], 'contains': ['24.b1', '36.a1', '36.c1', '36.e1'], 'core': '12.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6866, 2510, 5180, 2969], 'generators': [324, 42, 36, 216], 'label': '648.496.12.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1', 'normal_contained_in': ['4.a1', '6.b1', '6.d1', '6.e1'], 'normal_contains': ['24.b1', '36.a1', '36.c1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '324.144', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110386623
    {'ambient': '648.496', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '324.a1', 'complements': ['324.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '6.d1', '6.h1', '6.i1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7418, 2628, 7997, 4014], 'generators': [3, 216, 36, 324, 2, 42], 'label': '648.496.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.d1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '324.144'}
  • id: 110386624
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '36.10', 'aut_weyl_index': 648, 'centralizer': '18.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '6.c1', '6.i1', '6.k1'], 'contains': ['24.c1', '36.b1', '36.c1', '36.h1'], 'core': '12.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5183, 4233, 4175, 4616], 'generators': [324, 2, 42, 36], 'label': '648.496.12.c1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1', 'normal_contained_in': ['4.a1', '6.c1'], 'normal_contains': ['24.c1', '36.b1', '36.c1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 110386625
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.f1'], 'contains': ['24.d1', '36.a1', '36.f1', '36.h1'], 'core': '36.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1890, -1, 1130, -1], 'generators': [324, 44, 36, 216], 'label': '648.496.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.d1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386626
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 648, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '6.g1'], 'contains': ['24.e1', '36.c1', '36.g1', '36.h1'], 'core': '36.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [2725, -1, 2652, -1], 'generators': [324, 218, 42, 36], 'label': '648.496.12.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.e1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 110386627
    {'ambient': '648.496', 'aut_centralizer_order': 162, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 324, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.a1'], 'contains': ['24.a1', '36.i1', '36.l1', '36.m1', '36.o1'], 'core': '24.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2256, -1, 3005, -1], 'generators': [54, 2, 36, 216], 'label': '648.496.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.f1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386628
    {'ambient': '648.496', 'aut_centralizer_order': 54, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '6.b1'], 'contains': ['24.b1', '36.j1', '36.l1', '36.n1'], 'core': '24.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4502, -1, 3489, -1], 'generators': [54, 42, 36, 216], 'label': '648.496.12.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.g1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386629
    {'ambient': '648.496', 'aut_centralizer_order': 54, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.f1'], 'contains': ['24.d1', '36.k1', '36.l1', '36.p1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1024, -1, 646, -1], 'generators': [54, 44, 36, 216], 'label': '648.496.12.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.h1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386630
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 648, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.b1', '6.c1'], 'contains': ['24.c1', '36.m1', '36.n1', '36.p1'], 'core': '24.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [3157, -1, 1873, -1], 'generators': [54, 2, 42, 36], 'label': '648.496.12.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.i1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 110386631
    {'ambient': '648.496', 'aut_centralizer_order': 54, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 648, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '6.g1'], 'contains': ['24.e1', '36.n1', '36.o1', '36.p1'], 'core': '72.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [1421, -1, 1483, -1], 'generators': [54, 218, 42, 36], 'label': '648.496.12.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.j1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 110386632
    {'ambient': '648.496', 'aut_centralizer_order': 18, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.h1'], 'contains': ['24.a1', '36.q1', '36.r1', '36.t1'], 'core': '24.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7450, -1, 9622, -1], 'generators': [3, 2, 36, 216], 'label': '648.496.12.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '12.k1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 110386633
    {'ambient': '648.496', 'aut_centralizer_order': 12, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['4.c1', '6.i1'], 'contains': ['24.c1', '36.r1', '36.u1'], 'core': '24.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [8336, -1, 9351, -1], 'generators': [3, 2, 42, 36], 'label': '648.496.12.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '12.l1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 110386634
    {'ambient': '648.496', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '324.a1', 'complements': ['324.b1', '324.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.e1', '6.j1', '6.k1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6134, 4253, 5798, 588], 'generators': [93, 216, 36, 2, 324, 42], 'label': '648.496.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.e1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '324.144'}
  • id: 110386635
    {'ambient': '648.496', 'aut_centralizer_order': 2, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '5832.et', 'aut_weyl_index': 4, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '6.d1'], 'contains': ['24.b1', '36.s1', '36.t1', '36.u1'], 'core': '24.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9745, -1, 9904, -1], 'generators': [3, 42, 36, 216], 'label': '648.496.12.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '12.m1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1', 'subgroup_fusion': None, 'weyl_group': '162.40'}
  • id: 110386636
    {'ambient': '648.496', 'aut_centralizer_order': 972, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.b1', '6.f1', '9.d1'], 'contains': ['36.a1', '36.l1', '54.a1', '54.b1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4231, 8524, 3731, 8937], 'generators': [54, 324, 36, 216], 'label': '648.496.18.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1', 'normal_contained_in': ['6.a1', '6.b1'], 'normal_contains': ['36.a1', '54.a1', '54.b1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386637
    {'ambient': '648.496', 'aut_centralizer_order': 972, 'aut_label': '18.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '6.a1', 'complements': ['36.s1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.c1', '9.b1'], 'contains': ['36.b1', '36.m1', '54.b1', '54.c1'], 'core': '18.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4595, 7718, 4454, 8165], 'generators': [54, 324, 2, 36], 'label': '648.496.18.b1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.b1', 'normal_contained_in': ['6.a1', '6.c1'], 'normal_contains': ['36.b1', '54.b1'], 'normalizer': '1.a1', 'old_label': '18.b1', 'projective_image': '324.144', 'quotient_action_image': '6.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386638
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '6.b1', 'complements': ['36.q1'], 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '6.c1', '6.g1', '9.e1'], 'contains': ['36.c1', '36.n1', '54.b1', '54.d1'], 'core': '18.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [5643, 6910, 3897, 7393], 'generators': [54, 324, 42, 36], 'label': '648.496.18.c1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1', 'normal_contained_in': ['6.b1', '6.c1'], 'normal_contains': ['36.c1', '54.b1'], 'normalizer': '1.a1', 'old_label': '18.c1', 'projective_image': '324.144', 'quotient_action_image': '6.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110386639
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2916, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.d1', '36.i1', '54.a1', '54.c1', '54.e1'], 'core': '54.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3512, -1, 4938, -1], 'generators': [54, 324, 2, 252], 'label': '648.496.18.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.d1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386640
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.b1', '9.c1'], 'contains': ['36.e1', '36.j1', '54.a1', '54.d1'], 'core': '54.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7387, -1, 5422, -1], 'generators': [54, 324, 42, 252], 'label': '648.496.18.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '18.e1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386641
    {'ambient': '648.496', 'aut_centralizer_order': 54, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.f1'], 'contains': ['36.f1', '36.k1', '54.a1', '54.f1'], 'core': '54.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [505, -1, 404, -1], 'generators': [54, 324, 44, 252], 'label': '648.496.18.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '18.f1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386642
    {'ambient': '648.496', 'aut_centralizer_order': 486, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.g1'], 'contains': ['36.g1', '36.o1', '54.b1', '54.e1'], 'core': '54.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2345, -1, 3247, -1], 'generators': [54, 324, 218, 36], 'label': '648.496.18.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '18.g1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386643
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.c1', '6.f1', '6.g1'], 'contains': ['36.h1', '36.p1', '54.b1', '54.f1'], 'core': '54.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1167, -1, 888, -1], 'generators': [54, 324, 44, 36], 'label': '648.496.18.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '18.h1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386644
    {'ambient': '648.496', 'aut_centralizer_order': 36, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.h1', '9.a1'], 'contains': ['36.d1', '36.q1', '54.g1', '54.h1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6509, -1, 8106, -1], 'generators': [3, 324, 2, 252], 'label': '648.496.18.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.i1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386645
    {'ambient': '648.496', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '324.a1', 'complements': ['216.c1', '216.e1', '216.f1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.b1', '6.d1', '6.e1', '9.c1', '9.d1', '9.e1'], 'core': '3.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8406, 1949, 7057, 2198], 'generators': [3, 216, 36, 54, 324, 42], 'label': '648.496.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.b1', '6.d1', '6.e1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '324.144', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '324.144'}
  • id: 110386646
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1', '6.i1', '9.b1'], 'contains': ['36.b1', '36.r1', '54.g1', '54.i1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7113, -1, 7834, -1], 'generators': [3, 324, 2, 36], 'label': '648.496.18.j1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.j1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386647
    {'ambient': '648.496', 'aut_centralizer_order': 4, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.d1', '9.c1'], 'contains': ['36.e1', '36.s1', '54.h1', '54.j1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9129, -1, 9081, -1], 'generators': [3, 324, 42, 252], 'label': '648.496.18.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.k1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 110386648
    {'ambient': '648.496', 'aut_centralizer_order': 36, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '6.h1', '9.d1'], 'contains': ['36.a1', '36.t1', '54.h1', '54.i1'], 'core': '36.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8325, -1, 8411, -1], 'generators': [3, 324, 36, 216], 'label': '648.496.18.l1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.l1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 110386649
    {'ambient': '648.496', 'aut_centralizer_order': 12, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.d1', '6.i1', '9.e1'], 'contains': ['36.c1', '36.u1', '54.i1', '54.j1'], 'core': '36.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [9579, -1, 8746, -1], 'generators': [3, 324, 42, 36], 'label': '648.496.18.m1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.m1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 110386650
    {'ambient': '648.496', 'aut_centralizer_order': 36, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.j1', '9.a1'], 'contains': ['36.d1', '54.k1', '54.m1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5412, -1, 6466, -1], 'generators': [93, 2, 324, 252], 'label': '648.496.18.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.n1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386651
    {'ambient': '648.496', 'aut_centralizer_order': 4, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.e1', '9.c1'], 'contains': ['36.e1', '54.k1', '54.n1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8726, -1, 6748, -1], 'generators': [417, 324, 42, 252], 'label': '648.496.18.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '18.o1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 110386652
    {'ambient': '648.496', 'aut_centralizer_order': 36, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1', '6.j1', '9.d1'], 'contains': ['36.a1', '54.k1', '54.l1'], 'core': '36.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6883, -1, 5955, -1], 'generators': [417, 324, 36, 216], 'label': '648.496.18.p1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.p1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 110386653
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1', '6.k1', '9.b1'], 'contains': ['36.b1', '54.l1', '54.m1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [6085, -1, 5673, -1], 'generators': [93, 2, 324, 36], 'label': '648.496.18.q1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.q1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386654
    {'ambient': '648.496', 'aut_centralizer_order': 12, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['6.e1', '6.k1', '9.e1'], 'contains': ['36.c1', '54.l1', '54.n1'], 'core': '36.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [7852, -1, 6183, -1], 'generators': [417, 324, 42, 36], 'label': '648.496.18.r1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.r1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 110386655
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 324, 'centralizer': '6.a1', 'complements': ['27.d1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.a1', '12.f1', '12.k1'], 'contains': ['72.a1', '72.b1', '72.d1', '72.g1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3095, 4055, 3540, 3299], 'generators': [2, 36, 216], 'label': '648.496.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['72.a1', '72.b1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '648.496', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386656
    {'ambient': '648.496', 'aut_centralizer_order': 9, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.4033', 'aut_weyl_index': 27, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.h1', '6.j1', '9.a1', '9.b1', '9.d1'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6344, -1, 6667, -1], 'generators': [3, 216, 36, 54, 2, 324], 'label': '648.496.3.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '3.b1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 110386657
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '24.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 108, 'centralizer': '6.b1', 'complements': ['27.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1', '12.g1', '12.m1'], 'contains': ['72.a1', '72.c1', '72.e1'], 'core': '24.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5149, 807, 4254, 1849], 'generators': [42, 36, 216], 'label': '648.496.24.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1', 'normal_contained_in': ['8.a1', '12.b1'], 'normal_contains': ['72.a1', '72.c1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '648.496', 'quotient_action_image': '6.2', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110386658
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '36.10', 'aut_weyl_index': 648, 'centralizer': '18.a1', 'complements': ['27.b1', '27.d1'], 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '12.c1', '12.i1', '12.l1'], 'contains': ['72.b1', '72.c1', '72.h1'], 'core': '24.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [4299, 1595, 2561, 2574], 'generators': [2, 42], 'label': '648.496.24.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': ['8.a1', '12.c1'], 'normal_contains': ['72.b1', '72.c1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '648.496', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.5', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 110386659
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.d1', '12.h1'], 'contains': ['72.a1', '72.f1', '72.h1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1435, -1, 1162, -1], 'generators': [44, 36, 216], 'label': '648.496.24.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.d1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386660
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 648, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '12.e1', '12.j1'], 'contains': ['72.c1', '72.g1', '72.h1'], 'core': '72.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [2598, -1, 1592, -1], 'generators': [218, 42], 'label': '648.496.24.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.e1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 110386661
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2916, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1'], 'contains': ['54.c1', '54.g1', '54.m1', '81.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5846, -1, 7000, -1], 'generators': [3, 54, 2, 324], 'label': '648.496.27.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 110386662
    {'ambient': '648.496', 'aut_centralizer_order': 36, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.a1', '9.c1', '9.d1'], 'contains': ['54.a1', '54.h1', '54.k1', '81.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8111, -1, 7418, -1], 'generators': [3, 54, 324, 252], 'label': '648.496.27.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '27.b1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386663
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '9.d1', '9.e1'], 'contains': ['54.b1', '54.i1', '54.l1', '81.a1'], 'core': '54.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8706, -1, 7232, -1], 'generators': [3, 54, 324, 36], 'label': '648.496.27.c1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '27.c1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386664
    {'ambient': '648.496', 'aut_centralizer_order': 12, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.c1', '9.e1'], 'contains': ['54.d1', '54.j1', '54.n1', '81.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9389, -1, 7604, -1], 'generators': [3, 54, 324, 78], 'label': '648.496.27.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '27.d1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386665
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.b1', '12.d1', '18.a1', '18.l1', '18.p1'], 'contains': ['72.a1', '108.a1', '108.b1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5526, 6330, 5023, 6885], 'generators': [324, 36, 216], 'label': '648.496.36.a1', 'mobius_quo': -3, 'mobius_sub': 6, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '12.b1', '18.a1'], 'normal_contains': ['72.a1', '108.a1', '108.b1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386687
    {'ambient': '648.496', 'aut_centralizer_order': 12, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.l1', '12.m1', '18.m1'], 'contains': ['72.c1', '108.o1', '108.p1'], 'core': '72.c1', 'coset_action_label': None, 'count': 18, 'diagramx': [9890, -1, 9218, -1], 'generators': [3, 42, 36], 'label': '648.496.36.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1', 'old_label': '36.u1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
  • id: 110386666
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '36.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.c1', '18.b1', '18.j1', '18.q1'], 'contains': ['72.b1', '108.b1', '108.c1'], 'core': '36.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4989, 4991, 5572, 5605], 'generators': [324, 2, 36], 'label': '648.496.36.b1', 'mobius_quo': 0, 'mobius_sub': 54, 'normal_closure': '36.b1', 'normal_contained_in': ['12.a1', '12.c1', '18.b1'], 'normal_contains': ['72.b1', '108.b1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '324.144', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386667
    {'ambient': '648.496', 'aut_centralizer_order': 6, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '432.545', 'aut_weyl_index': 54, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['6.c1', '6.i1', '6.k1', '9.b1', '9.e1'], 'core': '6.c1', 'coset_action_label': None, 'count': 9, 'diagramx': [6653, -1, 6332, -1], 'generators': [3, 36, 42, 54, 2, 324], 'label': '648.496.3.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '3.c1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
  • id: 110386668
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '36.c1', 'aut_quo_index': 2, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['12.b1', '12.c1', '12.e1', '18.c1', '18.m1', '18.r1'], 'contains': ['72.c1', '108.b1', '108.d1'], 'core': '36.c1', 'coset_action_label': None, 'count': 3, 'diagramx': [6527, 2904, 5297, 4325], 'generators': [324, 42, 36], 'label': '648.496.36.c1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.c1', 'normal_contained_in': ['12.b1', '12.c1', '18.c1'], 'normal_contains': ['72.c1', '108.b1'], 'normalizer': '1.a1', 'old_label': '36.c1', 'projective_image': '324.144', 'quotient_action_image': '6.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 110386669
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.a1', '18.d1', '18.i1', '18.n1'], 'contains': ['72.d1', '108.a1', '108.c1', '108.e1'], 'core': '108.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4055, -1, 6395, -1], 'generators': [324, 2, 252], 'label': '648.496.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '36.d1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386670
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.b1', '18.e1', '18.k1', '18.o1'], 'contains': ['72.e1', '108.a1', '108.d1'], 'core': '108.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7993, -1, 6669, -1], 'generators': [324, 42, 252], 'label': '648.496.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.e1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386671
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.d1', '18.f1'], 'contains': ['72.f1', '108.a1', '108.f1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [505, -1, 668, -1], 'generators': [324, 44, 252], 'label': '648.496.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '36.f1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386672
    {'ambient': '648.496', 'aut_centralizer_order': 972, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.e1', '18.g1'], 'contains': ['72.g1', '108.b1', '108.e1'], 'core': '108.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2124, -1, 3045, -1], 'generators': [324, 218, 36], 'label': '648.496.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.g1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386673
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.c1', '12.d1', '12.e1', '18.h1'], 'contains': ['72.h1', '108.b1', '108.f1'], 'core': '108.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1547, -1, 1382, -1], 'generators': [324, 44, 36], 'label': '648.496.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.h1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386674
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.f1', '18.d1'], 'contains': ['72.d1', '108.g1', '108.i1', '108.k1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1870, -1, 3759, -1], 'generators': [54, 2, 252], 'label': '648.496.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '36.i1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386675
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.g1', '18.e1'], 'contains': ['72.e1', '108.g1', '108.j1'], 'core': '216.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5850, -1, 4474, -1], 'generators': [54, 42, 252], 'label': '648.496.36.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '36.j1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386676
    {'ambient': '648.496', 'aut_centralizer_order': 54, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '18.f1'], 'contains': ['72.f1', '108.g1', '108.l1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [110, -1, 119, -1], 'generators': [54, 44, 252], 'label': '648.496.36.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '36.k1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386677
    {'ambient': '648.496', 'aut_centralizer_order': 972, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '2.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.g1', '12.h1', '18.a1'], 'contains': ['72.a1', '108.g1', '108.h1'], 'core': '72.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2589, -1, 2077, -1], 'generators': [54, 36, 216], 'label': '648.496.36.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.l1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386678
    {'ambient': '648.496', 'aut_centralizer_order': 36, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '648.555', 'aut_weyl_index': 36, 'centralizer': '18.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '12.a1', '12.b1', '12.c1', '12.d1', '12.e1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4614, 4253, 4175, 3995], 'generators': [324, 36, 2, 42, 216], 'label': '648.496.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.a1', '12.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 110386679
    {'ambient': '648.496', 'aut_centralizer_order': 972, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '12.i1', '18.b1'], 'contains': ['72.b1', '108.h1', '108.i1'], 'core': '72.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [3054, -1, 2771, -1], 'generators': [54, 2, 36], 'label': '648.496.36.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.m1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386680
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.g1', '12.i1', '12.j1', '18.c1'], 'contains': ['72.c1', '108.h1', '108.j1'], 'core': '72.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [3731, -1, 2351, -1], 'generators': [54, 42, 36], 'label': '648.496.36.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.n1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386681
    {'ambient': '648.496', 'aut_centralizer_order': 486, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.f1', '12.j1', '18.g1'], 'contains': ['72.g1', '108.h1', '108.k1'], 'core': '216.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1152, -1, 1802, -1], 'generators': [54, 218, 36], 'label': '648.496.36.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.o1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386682
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.h1', '12.i1', '12.j1', '18.h1'], 'contains': ['72.h1', '108.h1', '108.l1'], 'core': '216.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [828, -1, 942, -1], 'generators': [54, 44, 36], 'label': '648.496.36.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.p1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 110386683
    {'ambient': '648.496', 'aut_centralizer_order': 36, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.k1', '18.i1'], 'contains': ['72.d1', '108.m1', '108.n1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6992, -1, 8806, -1], 'generators': [3, 2, 252], 'label': '648.496.36.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1', 'old_label': '36.q1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386684
    {'ambient': '648.496', 'aut_centralizer_order': 108, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.l1', '18.j1'], 'contains': ['72.b1', '108.m1', '108.o1'], 'core': '72.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [7599, -1, 8534, -1], 'generators': [3, 2, 36], 'label': '648.496.36.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1', 'old_label': '36.r1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 110386685
    {'ambient': '648.496', 'aut_centralizer_order': 4, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['12.m1', '18.k1'], 'contains': ['72.e1', '108.n1', '108.p1'], 'core': '216.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9721, -1, 9402, -1], 'generators': [3, 42, 252], 'label': '648.496.36.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.k1', 'old_label': '36.s1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 110386686
    {'ambient': '648.496', 'aut_centralizer_order': 36, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1', '12.m1', '18.l1'], 'contains': ['72.a1', '108.n1', '108.o1'], 'core': '72.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8701, -1, 9035, -1], 'generators': [3, 36, 216], 'label': '648.496.36.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1', 'old_label': '36.t1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 110386688
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '2.a1', 'complements': ['12.l1'], 'conjugacy_class_count': 3, 'contained_in': ['18.a1', '18.d1', '18.e1', '18.f1', '27.b1'], 'contains': ['108.a1', '108.g1', '162.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3590, 8524, 4748, 9445], 'generators': [54, 324, 252], 'label': '648.496.54.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.a1', 'normal_contained_in': ['18.a1'], 'normal_contains': ['108.a1', '162.a1'], 'normalizer': '1.a1', 'old_label': '54.a1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '27.3', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386689
    {'ambient': '648.496', 'aut_centralizer_order': 18, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '648.555', 'aut_weyl_index': 36, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '12.f1', '12.g1', '12.h1', '12.i1', '12.j1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3157, -1, 2262, -1], 'generators': [54, 36, 2, 42, 216], 'label': '648.496.4.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '4.b1', 'projective_image': '648.496', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 110386690
    {'ambient': '648.496', 'aut_centralizer_order': 5832, 'aut_label': '54.b1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.b1', '18.c1', '18.g1', '18.h1', '27.c1'], 'contains': ['108.b1', '108.h1', '162.a1'], 'core': '54.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4126, 7185, 3320, 8165], 'generators': [54, 324, 36], 'label': '648.496.54.b1', 'mobius_quo': 0, 'mobius_sub': 27, 'normal_closure': '54.b1', 'normal_contained_in': ['18.a1', '18.b1', '18.c1'], 'normal_contains': ['108.b1', '162.a1'], 'normalizer': '1.a1', 'old_label': '54.b1', 'projective_image': '324.144', 'quotient_action_image': '2.1', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386691
    {'ambient': '648.496', 'aut_centralizer_order': 1944, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '18.d1', '27.a1'], 'contains': ['108.c1', '108.i1', '162.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4874, -1, 5846, -1], 'generators': [54, 324, 2], 'label': '648.496.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.c1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386692
    {'ambient': '648.496', 'aut_centralizer_order': 648, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '6.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.c1', '18.e1', '27.d1'], 'contains': ['108.d1', '108.j1', '162.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7160, -1, 6121, -1], 'generators': [54, 324, 78], 'label': '648.496.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.d1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386693
    {'ambient': '648.496', 'aut_centralizer_order': 972, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '6.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '18.g1'], 'contains': ['108.e1', '108.k1', '162.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2559, -1, 4034, -1], 'generators': [54, 324, 218], 'label': '648.496.54.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '54.e1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386694
    {'ambient': '648.496', 'aut_centralizer_order': 324, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '6.f1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.f1', '18.h1'], 'contains': ['108.f1', '108.l1', '162.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [598, -1, 393, -1], 'generators': [54, 324, 44], 'label': '648.496.54.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '54.f1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 110386695
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '54.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1', '18.j1', '27.a1'], 'contains': ['108.c1', '108.m1', '162.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6211, -1, 7824, -1], 'generators': [3, 324, 2], 'label': '648.496.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.g1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 110386696
    {'ambient': '648.496', 'aut_centralizer_order': 72, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.i1', '18.k1', '18.l1', '27.b1'], 'contains': ['108.a1', '108.n1', '162.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8169, -1, 8179, -1], 'generators': [3, 324, 252], 'label': '648.496.54.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.h1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386697
    {'ambient': '648.496', 'aut_centralizer_order': 216, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1', '18.l1', '18.m1', '27.c1'], 'contains': ['108.b1', '108.o1', '162.b1'], 'core': '108.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8939, -1, 8034, -1], 'generators': [3, 324, 36], 'label': '648.496.54.i1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.i1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386698
    {'ambient': '648.496', 'aut_centralizer_order': 24, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.k1', '18.m1', '27.d1'], 'contains': ['108.d1', '108.p1', '162.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9402, -1, 8324, -1], 'generators': [3, 324, 78], 'label': '648.496.54.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.d1', 'old_label': '54.j1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 110386699
    {'ambient': '648.496', 'aut_centralizer_order': 72, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.n1', '18.o1', '18.p1', '27.b1'], 'contains': ['108.a1', '162.c1'], 'core': '108.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6877, -1, 7263, -1], 'generators': [417, 324, 252], 'label': '648.496.54.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.k1', 'projective_image': '324.144', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1', 'subgroup_fusion': None, 'weyl_group': '12.4'}