Formats: - HTML - YAML - JSON - 2026-07-22T05:01:20.145379
  • gps_groups • Show schema
    {'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': 36, 'aut_gen_orders': [12, 6, 18, 12], 'aut_gens': [[1, 6, 54], [257, 450, 510], [175, 12, 414], [865, 48, 378], [11, 864, 210]], 'aut_group': None, 'aut_hash': 1462454001501625696, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 104976, 'aut_permdeg': 180, 'aut_perms': [182284697248881600225277212548653441934643334532640347557620701025183743544604131553139247417321102426786243262151216358080107690298050747572879947045571419874984552048597452343734911848023050837028953335258457843198126483105821547138026258397459286374574976932506776614877626011877954562409483742196179449644767169863263393743791, 186199637125001788386724309028522268508347973322643831113444393984012606643890015375650342708151571402675126840547707820397474964060022192523988986602739235889084158234417861641575142113174592626127582053437157099799894101918563828178097644949818825974660535504942854931801097002291774337390343066981931199043826088657445393311727, 87772501514757875061997135623309057011100136756167617242327965267782473605045922639073170085732164319661187832826734916508516418179827174647028483528044812806848130000672902503931302216303170851958299068724406786630667596783577487986461764662910260931380981979096783133868262083546169893760040507792919333479420982014368764928838, 159373207695967153406972289933948769813634491254304994409998355312487498335457006892642199177209231494370090700307501039300735491715320739772931264170579672441420875283366740535798028076690530617646058316986059204303568230292640376049563932716338473766890176133217754587517271160396937523310899833920648729110338699664471611990205], 'aut_phi_ratio': 324.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 81, 2, 1], [3, 2, 2, 2], [3, 9, 2, 1], [6, 2, 2, 2], [6, 9, 2, 1], [6, 81, 4, 1], [9, 6, 6, 2], [9, 18, 2, 2], [9, 18, 4, 1], [18, 6, 6, 2], [18, 18, 2, 2], [18, 18, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_9^2.C_3^3.C_6.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': None, 'autcentquo_hash': 6058086793834862908, 'autcentquo_nilpotent': False, 'autcentquo_order': 52488, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_9^2.C_3^3.C_6.C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 81, 2], [3, 2, 4], [3, 9, 2], [6, 2, 4], [6, 9, 2], [6, 81, 4], [9, 6, 12], [9, 18, 8], [18, 6, 12], [18, 18, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '486.154', 'commutator_count': 1, 'commutator_label': '81.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 655, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['486.154', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 81, 1, 2], [3, 2, 1, 4], [3, 9, 2, 1], [6, 2, 1, 4], [6, 9, 2, 1], [6, 81, 2, 2], [9, 6, 1, 6], [9, 6, 3, 2], [9, 18, 2, 4], [18, 6, 1, 6], [18, 6, 3, 2], [18, 18, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3276, 'exponent': 18, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '108.43', 'hash': 655, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 9, 9], 'inner_gens': [[1, 12, 270], [49, 6, 54], [757, 6, 54]], 'inner_hash': 154, 'inner_nilpotent': False, 'inner_order': 486, 'inner_split': False, 'inner_tex': 'C_9^2:C_6', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 12], [2, 24], [6, 24]], 'label': '972.655', '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': 'C2*C9^2: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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 60, 'number_divisions': 40, 'number_normal_subgroups': 52, 'number_subgroup_autclasses': 80, 'number_subgroup_classes': 204, 'number_subgroups': 1968, 'old_label': None, 'order': 972, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 163], [3, 26], [6, 350], [9, 216], [18, 216]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6, 6, 6], 'outer_gen_pows': [3, 0, 0], 'outer_gens': [[5, 108, 492], [5, 108, 840], [487, 654, 90]], 'outer_group': '216.170', 'outer_hash': 170, 'outer_nilpotent': False, 'outer_order': 216, 'outer_permdeg': 11, 'outer_perms': [8427606, 15729888, 11980801], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times S_3^2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 12], [4, 8], [6, 12], [18, 4]], 'representations': {'PC': {'code': 25153952859197068134499589496877266513156795, 'gens': [1, 3, 5], 'pres': [7, -2, -3, -3, -3, -2, -3, -3, 14, 254, 261, 79, 1011, 9454, 6626, 102, 22685, 15888, 166, 31758]}, 'Perm': {'d': 20, 'gens': [122738329117168687, 3628800, 270008871745557064, 68895, 385590117980492756, 151397, 512275163533056000]}}, 'schur_multiplier': [18], '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_2\\times C_9^2:C_6', 'transitive_degree': 162, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 143963610
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 655, 'group_order': 972, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 143963621
      {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 655, 'group_order': 972, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 486, 'size': 1}
    • id: 143963632
      {'aut_label': '2B', 'centralizer': '81.a1', 'counter': 3, 'group_counter': 655, 'group_order': 972, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 597, 'size': 81}
    • id: 143963643
      {'aut_label': '2B', 'centralizer': '81.a1', 'counter': 4, 'group_counter': 655, 'group_order': 972, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 327, 'size': 81}
    • id: 143963654
      {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 5, 'group_counter': 655, 'group_order': 972, 'label': '3A', 'order': 3, 'powers': [5, 1], 'representative': 324, 'size': 2}
    • id: 143963665
      {'aut_label': '3A', 'centralizer': '2.a1', 'counter': 6, 'group_counter': 655, 'group_order': 972, 'label': '3B', 'order': 3, 'powers': [6, 1], 'representative': 36, 'size': 2}
    • id: 143963667
      {'aut_label': '3C', 'centralizer': '2.a1', 'counter': 7, 'group_counter': 655, 'group_order': 972, 'label': '3C', 'order': 3, 'powers': [7, 1], 'representative': 360, 'size': 2}
    • id: 143963668
      {'aut_label': '3C', 'centralizer': '2.a1', 'counter': 8, 'group_counter': 655, 'group_order': 972, 'label': '3D', 'order': 3, 'powers': [8, 1], 'representative': 342, 'size': 2}
    • id: 143963669
      {'aut_label': '3E1', 'centralizer': '9.b1', 'counter': 9, 'group_counter': 655, 'group_order': 972, 'label': '3E1', 'order': 3, 'powers': [10, 1], 'representative': 328, 'size': 9}
    • id: 143963611
      {'aut_label': '3E1', 'centralizer': '9.b1', 'counter': 10, 'group_counter': 655, 'group_order': 972, 'label': '3E-1', 'order': 3, 'powers': [9, 1], 'representative': 650, 'size': 9}
    • id: 143963612
      {'aut_label': '6A', 'centralizer': '2.a1', 'counter': 11, 'group_counter': 655, 'group_order': 972, 'label': '6A', 'order': 6, 'powers': [5, 2], 'representative': 162, 'size': 2}
    • id: 143963613
      {'aut_label': '6A', 'centralizer': '2.a1', 'counter': 12, 'group_counter': 655, 'group_order': 972, 'label': '6B', 'order': 6, 'powers': [6, 2], 'representative': 504, 'size': 2}
    • id: 143963614
      {'aut_label': '6C', 'centralizer': '2.a1', 'counter': 13, 'group_counter': 655, 'group_order': 972, 'label': '6C', 'order': 6, 'powers': [7, 2], 'representative': 180, 'size': 2}
    • id: 143963615
      {'aut_label': '6C', 'centralizer': '2.a1', 'counter': 14, 'group_counter': 655, 'group_order': 972, 'label': '6D', 'order': 6, 'powers': [8, 2], 'representative': 198, 'size': 2}
    • id: 143963616
      {'aut_label': '6E1', 'centralizer': '9.b1', 'counter': 15, 'group_counter': 655, 'group_order': 972, 'label': '6E1', 'order': 6, 'powers': [9, 2], 'representative': 164, 'size': 9}
    • id: 143963617
      {'aut_label': '6E1', 'centralizer': '9.b1', 'counter': 16, 'group_counter': 655, 'group_order': 972, 'label': '6E-1', 'order': 6, 'powers': [10, 2], 'representative': 166, 'size': 9}
    • id: 143963618
      {'aut_label': '6F1', 'centralizer': '81.a1', 'counter': 17, 'group_counter': 655, 'group_order': 972, 'label': '6F1', 'order': 6, 'powers': [10, 3], 'representative': 271, 'size': 81}
    • id: 143963619
      {'aut_label': '6F1', 'centralizer': '81.a1', 'counter': 18, 'group_counter': 655, 'group_order': 972, 'label': '6F-1', 'order': 6, 'powers': [9, 3], 'representative': 923, 'size': 81}
    • id: 143963620
      {'aut_label': '6F1', 'centralizer': '81.a1', 'counter': 19, 'group_counter': 655, 'group_order': 972, 'label': '6G1', 'order': 6, 'powers': [10, 4], 'representative': 325, 'size': 81}
    • id: 143963622
      {'aut_label': '6F1', 'centralizer': '81.a1', 'counter': 20, 'group_counter': 655, 'group_order': 972, 'label': '6G-1', 'order': 6, 'powers': [9, 4], 'representative': 329, 'size': 81}
    • id: 143963623
      {'aut_label': '9A', 'centralizer': '6.c1', 'counter': 21, 'group_counter': 655, 'group_order': 972, 'label': '9A', 'order': 9, 'powers': [21, 5], 'representative': 108, 'size': 6}
    • id: 143963624
      {'aut_label': '9A', 'centralizer': '6.c1', 'counter': 22, 'group_counter': 655, 'group_order': 972, 'label': '9B', 'order': 9, 'powers': [22, 5], 'representative': 144, 'size': 6}
    • id: 143963625
      {'aut_label': '9A', 'centralizer': '6.c1', 'counter': 23, 'group_counter': 655, 'group_order': 972, 'label': '9C', 'order': 9, 'powers': [23, 5], 'representative': 126, 'size': 6}
    • id: 143963626
      {'aut_label': '9A', 'centralizer': '6.c1', 'counter': 24, 'group_counter': 655, 'group_order': 972, 'label': '9D', 'order': 9, 'powers': [24, 6], 'representative': 336, 'size': 6}
    • id: 143963627
      {'aut_label': '9A', 'centralizer': '6.c1', 'counter': 25, 'group_counter': 655, 'group_order': 972, 'label': '9E', 'order': 9, 'powers': [25, 6], 'representative': 348, 'size': 6}
    • id: 143963628
      {'aut_label': '9A', 'centralizer': '6.c1', 'counter': 26, 'group_counter': 655, 'group_order': 972, 'label': '9F', 'order': 9, 'powers': [26, 6], 'representative': 12, 'size': 6}
    • id: 143963629
      {'aut_label': '9G1', 'centralizer': '6.c1', 'counter': 27, 'group_counter': 655, 'group_order': 972, 'label': '9G1', 'order': 9, 'powers': [28, 7], 'representative': 120, 'size': 6}
    • id: 143963630
      {'aut_label': '9G1', 'centralizer': '6.c1', 'counter': 28, 'group_counter': 655, 'group_order': 972, 'label': '9G2', 'order': 9, 'powers': [29, 7], 'representative': 240, 'size': 6}
    • id: 143963631
      {'aut_label': '9G1', 'centralizer': '6.c1', 'counter': 29, 'group_counter': 655, 'group_order': 972, 'label': '9G4', 'order': 9, 'powers': [27, 7], 'representative': 480, 'size': 6}
    • id: 143963633
      {'aut_label': '9G1', 'centralizer': '6.c1', 'counter': 30, 'group_counter': 655, 'group_order': 972, 'label': '9H1', 'order': 9, 'powers': [31, 8], 'representative': 132, 'size': 6}
    • id: 143963634
      {'aut_label': '9G1', 'centralizer': '6.c1', 'counter': 31, 'group_counter': 655, 'group_order': 972, 'label': '9H2', 'order': 9, 'powers': [32, 8], 'representative': 264, 'size': 6}
    • id: 143963635
      {'aut_label': '9G1', 'centralizer': '6.c1', 'counter': 32, 'group_counter': 655, 'group_order': 972, 'label': '9H4', 'order': 9, 'powers': [30, 8], 'representative': 474, 'size': 6}
    • id: 143963636
      {'aut_label': '9I1', 'centralizer': '18.e1', 'counter': 33, 'group_counter': 655, 'group_order': 972, 'label': '9I1', 'order': 9, 'powers': [34, 5], 'representative': 436, 'size': 18}
    • id: 143963637
      {'aut_label': '9I-1', 'centralizer': '18.e1', 'counter': 34, 'group_counter': 655, 'group_order': 972, 'label': '9I-1', 'order': 9, 'powers': [33, 5], 'representative': 866, 'size': 18}
    • id: 143963638
      {'aut_label': '9J1', 'centralizer': '18.f1', 'counter': 35, 'group_counter': 655, 'group_order': 972, 'label': '9J1', 'order': 9, 'powers': [36, 7], 'representative': 466, 'size': 18}
    • id: 143963639
      {'aut_label': '9J1', 'centralizer': '18.f1', 'counter': 36, 'group_counter': 655, 'group_order': 972, 'label': '9J-1', 'order': 9, 'powers': [35, 7], 'representative': 908, 'size': 18}
    • id: 143963640
      {'aut_label': '9J1', 'centralizer': '18.f1', 'counter': 37, 'group_counter': 655, 'group_order': 972, 'label': '9K1', 'order': 9, 'powers': [38, 8], 'representative': 442, 'size': 18}
    • id: 143963641
      {'aut_label': '9J1', 'centralizer': '18.f1', 'counter': 38, 'group_counter': 655, 'group_order': 972, 'label': '9K-1', 'order': 9, 'powers': [37, 8], 'representative': 896, 'size': 18}
    • id: 143963642
      {'aut_label': '9I-1', 'centralizer': '18.e1', 'counter': 39, 'group_counter': 655, 'group_order': 972, 'label': '9L1', 'order': 9, 'powers': [40, 6], 'representative': 358, 'size': 18}
    • id: 143963644
      {'aut_label': '9I1', 'centralizer': '18.e1', 'counter': 40, 'group_counter': 655, 'group_order': 972, 'label': '9L-1', 'order': 9, 'powers': [39, 6], 'representative': 692, 'size': 18}
    • id: 143963645
      {'aut_label': '18A', 'centralizer': '6.c1', 'counter': 41, 'group_counter': 655, 'group_order': 972, 'label': '18A', 'order': 18, 'powers': [21, 11], 'representative': 54, 'size': 6}
    • id: 143963646
      {'aut_label': '18A', 'centralizer': '6.c1', 'counter': 42, 'group_counter': 655, 'group_order': 972, 'label': '18B', 'order': 18, 'powers': [22, 11], 'representative': 72, 'size': 6}
    • id: 143963647
      {'aut_label': '18A', 'centralizer': '6.c1', 'counter': 43, 'group_counter': 655, 'group_order': 972, 'label': '18C', 'order': 18, 'powers': [23, 11], 'representative': 90, 'size': 6}
    • id: 143963648
      {'aut_label': '18A', 'centralizer': '6.c1', 'counter': 44, 'group_counter': 655, 'group_order': 972, 'label': '18D', 'order': 18, 'powers': [24, 12], 'representative': 168, 'size': 6}
    • id: 143963649
      {'aut_label': '18A', 'centralizer': '6.c1', 'counter': 45, 'group_counter': 655, 'group_order': 972, 'label': '18E', 'order': 18, 'powers': [25, 12], 'representative': 174, 'size': 6}
    • id: 143963650
      {'aut_label': '18A', 'centralizer': '6.c1', 'counter': 46, 'group_counter': 655, 'group_order': 972, 'label': '18F', 'order': 18, 'powers': [26, 12], 'representative': 492, 'size': 6}
    • id: 143963651
      {'aut_label': '18G1', 'centralizer': '6.c1', 'counter': 47, 'group_counter': 655, 'group_order': 972, 'label': '18G1', 'order': 18, 'powers': [27, 13], 'representative': 60, 'size': 6}
    • id: 143963652
      {'aut_label': '18G1', 'centralizer': '6.c1', 'counter': 48, 'group_counter': 655, 'group_order': 972, 'label': '18G5', 'order': 18, 'powers': [29, 13], 'representative': 384, 'size': 6}
    • id: 143963653
      {'aut_label': '18G1', 'centralizer': '6.c1', 'counter': 49, 'group_counter': 655, 'group_order': 972, 'label': '18G7', 'order': 18, 'powers': [28, 13], 'representative': 78, 'size': 6}
    • id: 143963655
      {'aut_label': '18G1', 'centralizer': '6.c1', 'counter': 50, 'group_counter': 655, 'group_order': 972, 'label': '18H1', 'order': 18, 'powers': [30, 14], 'representative': 66, 'size': 6}
    • id: 143963656
      {'aut_label': '18G1', 'centralizer': '6.c1', 'counter': 51, 'group_counter': 655, 'group_order': 972, 'label': '18H5', 'order': 18, 'powers': [32, 14], 'representative': 276, 'size': 6}
    • id: 143963657
      {'aut_label': '18G1', 'centralizer': '6.c1', 'counter': 52, 'group_counter': 655, 'group_order': 972, 'label': '18H7', 'order': 18, 'powers': [31, 14], 'representative': 714, 'size': 6}
    • id: 143963658
      {'aut_label': '18I1', 'centralizer': '18.e1', 'counter': 53, 'group_counter': 655, 'group_order': 972, 'label': '18I1', 'order': 18, 'powers': [33, 11], 'representative': 56, 'size': 18}
    • id: 143963659
      {'aut_label': '18I-1', 'centralizer': '18.e1', 'counter': 54, 'group_counter': 655, 'group_order': 972, 'label': '18I-1', 'order': 18, 'powers': [34, 11], 'representative': 58, 'size': 18}
    • id: 143963660
      {'aut_label': '18J1', 'centralizer': '18.f1', 'counter': 55, 'group_counter': 655, 'group_order': 972, 'label': '18J1', 'order': 18, 'powers': [35, 13], 'representative': 62, 'size': 18}
    • id: 143963661
      {'aut_label': '18J1', 'centralizer': '18.f1', 'counter': 56, 'group_counter': 655, 'group_order': 972, 'label': '18J-1', 'order': 18, 'powers': [36, 13], 'representative': 64, 'size': 18}
    • id: 143963662
      {'aut_label': '18J1', 'centralizer': '18.f1', 'counter': 57, 'group_counter': 655, 'group_order': 972, 'label': '18K1', 'order': 18, 'powers': [37, 14], 'representative': 68, 'size': 18}
    • id: 143963663
      {'aut_label': '18J1', 'centralizer': '18.f1', 'counter': 58, 'group_counter': 655, 'group_order': 972, 'label': '18K-1', 'order': 18, 'powers': [38, 14], 'representative': 70, 'size': 18}
    • id: 143963664
      {'aut_label': '18I-1', 'centralizer': '18.e1', 'counter': 59, 'group_counter': 655, 'group_order': 972, 'label': '18L1', 'order': 18, 'powers': [39, 12], 'representative': 170, 'size': 18}
    • id: 143963666
      {'aut_label': '18I1', 'centralizer': '18.e1', 'counter': 60, 'group_counter': 655, 'group_order': 972, 'label': '18L-1', 'order': 18, 'powers': [40, 12], 'representative': 172, 'size': 18}
  • gps_qchar • Show schema
    • id: 13980392
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.1a', '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], 'schur_index': 1}
    • id: 13980403
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.1b', '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], 'schur_index': 1}
    • id: 13980414
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.1c', '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], 'schur_index': 1}
    • id: 13980425
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.1d', '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], 'schur_index': 1}
    • id: 13980427
      {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 13980428
      {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.1f', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, 2, 2, 2, -1, -1, -2, -2, -2, -2, 1, 1, 1, 1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 13980429
      {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, 2, 2, 2, -1, -1, -2, -2, -2, -2, 1, 1, -1, -1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 13980430
      {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, -1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 13980431
      {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
    • id: 13980393
      {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1], 'schur_index': 1}
    • id: 13980394
      {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1], 'schur_index': 1}
    • id: 13980395
      {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2], 'schur_index': 1}
    • id: 13980396
      {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1], 'schur_index': 1}
    • id: 13980397
      {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, -1, -1, 1, 1, 1, -2, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1], 'schur_index': 1}
    • id: 13980398
      {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 1, 1, -2, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, -2, 1, 1, 1, 1, -2, 1], 'schur_index': 1}
    • id: 13980399
      {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, -2], 'schur_index': 1}
    • id: 13980400
      {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2i', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, -2, -2, 4, 4, 4, 4, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, 4, -2, 4, 4, -2, 1, 1, 1, 1, 1, -2, 1, -2, -2, 4, -2, -2, 4, -2, -2, 4, -2, -2, -2, -2, -2, 1, 1, -2, 1, 1, 1, 1], 'schur_index': 1}
    • id: 13980401
      {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2j', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, -2, -2, 4, 4, 4, 4, -2, -2, 0, 0, 0, 0, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, 4, 1, 1, -2, 1, -2, 1, 1, 1, -2, -2, -2, 4, -2, 4, -2, -2, 4, -2, -2, -2, 1, 1, -2, 1, -2, 1, 1, 1], 'schur_index': 1}
    • id: 13980402
      {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2k', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, -2, -2, 4, 4, 4, 4, -2, -2, 0, 0, 0, 0, -2, -2, 4, -2, 4, -2, -2, -2, 4, -2, -2, -2, 1, -2, 1, -2, 1, 1, 1, 1, -2, -2, 4, -2, -2, -2, -2, -2, -2, 4, 4, -2, 1, -2, 1, 1, 1, 1, -2, 1], 'schur_index': 1}
    • id: 13980404
      {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2l', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, -2, -2, 4, 4, 4, 4, -2, -2, 0, 0, 0, 0, 4, 4, -2, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, 4, -2, -2, -2, -2, -2, 4, -2, -2, -2, -2, 4, 1, 1, 1, 1, 1, -2, 1, -2], 'schur_index': 1}
    • id: 13980405
      {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2m', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, -2, -2, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, 4, -2, 4, 4, -2, 1, 1, 1, 1, 1, -2, 1, -2, 2, -4, 2, 2, -4, 2, 2, -4, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
    • id: 13980406
      {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2n', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, -2, -2, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, 4, 1, 1, -2, 1, -2, 1, 1, 1, 2, 2, 2, -4, 2, -4, 2, 2, -4, 2, 2, 2, -1, -1, 2, -1, 2, -1, -1, -1], 'schur_index': 1}
    • id: 13980407
      {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2o', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, -2, -2, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, -2, -2, 4, -2, 4, -2, -2, -2, 4, -2, -2, -2, 1, -2, 1, -2, 1, 1, 1, 1, 2, 2, -4, 2, 2, 2, 2, 2, 2, -4, -4, 2, -1, 2, -1, -1, -1, -1, 2, -1], 'schur_index': 1}
    • id: 13980408
      {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.2p', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, -2, -2, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, 4, 4, -2, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, -4, 2, 2, 2, 2, 2, -4, 2, 2, 2, 2, -4, -1, -1, -1, -1, -1, 2, -1, 2], 'schur_index': 1}
    • id: 13980409
      {'cdim': 6, 'counter': 25, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6a', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -3, -3, -3, 6, 0, 0, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, -3, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980410
      {'cdim': 6, 'counter': 26, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6b', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -3, -3, -3, 6, 0, 0, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, -3, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980411
      {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6c', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -3, -3, -3, 6, 0, 0, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980412
      {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6d', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -3, 6, -3, -3, 0, 0, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980413
      {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6e', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -3, 6, -3, -3, 0, 0, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 6, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980415
      {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6f', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 0, 0, -3, 6, -3, -3, 0, 0, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, -3, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980416
      {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6g', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, -6, 0, 0, -3, -3, -3, 6, 0, 0, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, -3, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980417
      {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6h', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, -6, 0, 0, -3, -3, -3, 6, 0, 0, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, -3, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980418
      {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6i', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, -6, 0, 0, -3, -3, -3, 6, 0, 0, 3, 3, -6, 3, 0, 0, 0, 0, 0, 0, 6, -3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980419
      {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6j', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, -6, 0, 0, -3, 6, -3, -3, 0, 0, 3, 3, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980420
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    • id: 13980421
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    • id: 13980422
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    • id: 13980423
      {'cdim': 6, 'counter': 38, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6n', 'multiplicity': 3, 'nt': [27, 54], 'qdim': 18, 'qvalues': [18, 18, 0, 0, 18, -9, -9, -9, 0, 0, 18, -9, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980424
      {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6o', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -18, 0, 0, -9, -9, 18, -9, 0, 0, 9, -18, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 13980426
      {'cdim': 6, 'counter': 40, 'faithful': False, 'group': '972.655', 'group_order': 972, 'image': None, 'label': '972.655.6p', 'multiplicity': 3, 'nt': [54, 0], 'qdim': 18, 'qvalues': [18, -18, 0, 0, 18, -9, -9, -9, 0, 0, -18, 9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
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    • id: 33095903
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1', 'kernel_order': 162, 'label': '972.655.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 33095904
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 162, 'label': '972.655.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]]]}
    • id: 33095905
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 162, 'label': '972.655.2d', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]]]}
    • id: 33095906
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 81, 'label': '972.655.2e', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 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]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 33095907
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1', 'kernel_order': 81, 'label': '972.655.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 33095908
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 81, 'label': '972.655.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 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]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]]]}
    • id: 33095910
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 81, 'label': '972.655.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]]]}
    • id: 33095911
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 21, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 54, 'label': '972.655.2i1', 'nt': [6, 5], '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, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
    • id: 33095912
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 22, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 54, 'label': '972.655.2i2', 'nt': [6, 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, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
    • id: 33095913
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 23, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 54, 'label': '972.655.2j1', 'nt': [6, 5], '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, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
    • id: 33095914
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 24, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1', 'kernel_order': 54, 'label': '972.655.2j2', 'nt': [6, 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, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
    • id: 33095915
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 25, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 54, 'label': '972.655.2k1', 'nt': [6, 5], '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, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]]]}
    • id: 33095916
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 26, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 54, 'label': '972.655.2k2', 'nt': [6, 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, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]]]}
    • id: 33095917
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 27, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 54, 'label': '972.655.2l1', 'nt': [6, 5], '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, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[2, 1]]]}
    • id: 33095918
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 28, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1', 'kernel_order': 54, 'label': '972.655.2l2', 'nt': [6, 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, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]]]}
    • id: 33095919
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 29, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 27, 'label': '972.655.2m1', 'nt': [12, 18], '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, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[2, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, -1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
    • id: 33095921
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 30, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 27, 'label': '972.655.2m2', '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, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
    • id: 33095922
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 31, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 27, 'label': '972.655.2n1', 'nt': [12, 18], '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, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, -1]], [[1, 1]], [[-2, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
    • id: 33095923
      {'center': '6.b1', 'center_index': 6, 'center_order': 162, 'counter': 32, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 27, 'label': '972.655.2n2', '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, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-1, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 1]], [[1, -1]], [[-2, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
    • id: 33095924
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 33, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 27, 'label': '972.655.2o1', 'nt': [12, 18], '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, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[1, 1]]]}
    • id: 33095925
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 34, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 27, 'label': '972.655.2o2', '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, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[1, -1]]]}
    • id: 33095926
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 35, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 27, 'label': '972.655.2p1', 'nt': [12, 18], '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, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-2, -1]], [[1, -1]], [[-2, 1]]]}
    • id: 33095927
      {'center': '6.a1', 'center_index': 6, 'center_order': 162, 'counter': 36, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 27, 'label': '972.655.2p2', '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, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-2, 1]], [[1, 1]], [[-2, -1]]]}
    • id: 33095928
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 37, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 18, 'label': '972.655.6a', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095929
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 38, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 18, 'label': '972.655.6b', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095930
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 39, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 18, 'label': '972.655.6c', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095932
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 40, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 18, 'label': '972.655.6d', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095933
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 41, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 18, 'label': '972.655.6e', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095934
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 42, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1', 'kernel_order': 18, 'label': '972.655.6f', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095935
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 43, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 9, 'label': '972.655.6g', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095936
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 44, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 9, 'label': '972.655.6h', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[-3, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095937
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 45, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 9, 'label': '972.655.6i', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095938
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 46, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 9, 'label': '972.655.6j', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095939
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 47, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 9, 'label': '972.655.6k', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095940
      {'center': '54.a1', 'center_index': 54, 'center_order': 18, 'counter': 48, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1', 'kernel_order': 9, 'label': '972.655.6l', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095941
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 49, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '162.43', 'image_order': 162, 'indicator': 1, 'kernel': '162.b1', 'kernel_order': 6, 'label': '972.655.6m1', 'nt': [27, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 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]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095943
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 50, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '162.43', 'image_order': 162, 'indicator': 1, 'kernel': '162.b1', 'kernel_order': 6, 'label': '972.655.6m2', 'nt': [27, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 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]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095944
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 51, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '162.43', 'image_order': 162, 'indicator': 1, 'kernel': '162.b1', 'kernel_order': 6, 'label': '972.655.6m3', 'nt': [27, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 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]], [[3, 1], [3, -1]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095945
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 52, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '162.43', 'image_order': 162, 'indicator': 1, 'kernel': '162.b1', 'kernel_order': 6, 'label': '972.655.6n1', 'nt': [27, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095946
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 53, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '162.43', 'image_order': 162, 'indicator': 1, 'kernel': '162.b1', 'kernel_order': 6, 'label': '972.655.6n2', 'nt': [27, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095947
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 54, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '162.43', 'image_order': 162, 'indicator': 1, 'kernel': '162.b1', 'kernel_order': 6, 'label': '972.655.6n3', 'nt': [27, 54], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095948
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 55, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '324.147', 'image_order': 324, 'indicator': 1, 'kernel': '324.b1', 'kernel_order': 3, 'label': '972.655.6o1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 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]], [[3, 4], [3, -4]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095949
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 56, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '324.147', 'image_order': 324, 'indicator': 1, 'kernel': '324.b1', 'kernel_order': 3, 'label': '972.655.6o2', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 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]], [[3, 2], [3, -2]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[0, 0]], [[-3, 4], [-3, -4]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095950
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 57, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '324.147', 'image_order': 324, 'indicator': 1, 'kernel': '324.b1', 'kernel_order': 3, 'label': '972.655.6o3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 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]], [[3, 1], [3, -1]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095951
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 58, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '324.147', 'image_order': 324, 'indicator': 1, 'kernel': '324.b1', 'kernel_order': 3, 'label': '972.655.6p1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[3, 4], [3, -4]], [[0, 0]], [[3, 1], [3, -1]], [[3, 2], [3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095952
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 59, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '324.147', 'image_order': 324, 'indicator': 1, 'kernel': '324.b1', 'kernel_order': 3, 'label': '972.655.6p2', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[3, 2], [3, -2]], [[0, 0]], [[3, 4], [3, -4]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 33095954
      {'center': '162.b1', 'center_index': 162, 'center_order': 6, 'counter': 60, 'cyclotomic_n': 9, 'dim': 6, 'faithful': False, 'field': [-1, -3, 0, 1], 'group': '972.655', 'group_counter': 655, 'group_order': 972, 'image': None, 'image_isoclass': '324.147', 'image_order': 324, 'indicator': 1, 'kernel': '324.b1', 'kernel_order': 3, 'label': '972.655.6p3', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 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]], [[3, 1], [3, -1]], [[0, 0]], [[3, 2], [3, -2]], [[3, 4], [3, -4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[-3, 4], [-3, -4]], [[0, 0]], [[0, 0]], [[-3, 2], [-3, -2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • gps_subgroup_search • Show schema
    • id: 115726448
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 972, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '972.655.1.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': '972.655', 'subgroup_hash': 655, 'subgroup_order': 972, 'subgroup_tex': 'C_2\\times C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726459
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 486, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.2.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': '486.202', 'subgroup_hash': 202, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726470
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 486, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '972.655.2.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': '486.154', 'subgroup_hash': 154, 'subgroup_order': 486, 'subgroup_tex': 'C_9^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726481
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 324, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.3.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': '324.74', 'subgroup_hash': 74, 'subgroup_order': 324, 'subgroup_tex': 'C_9:D_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726492
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.3.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': '324.146', 'subgroup_hash': 146, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726503
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.3.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': '324.63', 'subgroup_hash': 63, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:D_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726514
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 243, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '972.655.4.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.43', 'subgroup_hash': 43, 'subgroup_order': 243, 'subgroup_tex': 'C_9^2:C_3', 'supersolvable': True, 'sylow': 3}
    • id: 115726525
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.6.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.49', 'subgroup_hash': 49, 'subgroup_order': 162, 'subgroup_tex': 'C_{18}:C_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 115726527
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.b1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.24', 'subgroup_hash': 24, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726449
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 162, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.c1', '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': '162.23', 'subgroup_hash': 23, 'subgroup_order': 162, 'subgroup_tex': 'C_9\\times C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726450
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 162, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.6.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': '162.16', 'subgroup_hash': 16, 'subgroup_order': 162, 'subgroup_tex': 'C_9:D_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726451
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.6.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '162.25', 'subgroup_hash': 25, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726452
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.6.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '162.25', 'subgroup_hash': 25, 'subgroup_order': 162, 'subgroup_tex': 'C_9:C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726453
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.6.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726454
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 81, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.6.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': '162.5', 'subgroup_hash': 5, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2:D_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726455
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.9.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': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726456
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726457
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.9.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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726458
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 54, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.9.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': '108.27', 'subgroup_hash': 27, 'subgroup_order': 108, 'subgroup_tex': 'C_3:D_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726460
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.12.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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 115726461
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.12.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': '12.4', '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': '81.3', 'subgroup_hash': 3, 'subgroup_order': 81, 'subgroup_tex': 'C_3^2:C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726462
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 81, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.2', 'subgroup_hash': 2, 'subgroup_order': 81, 'subgroup_tex': 'C_9^2', 'supersolvable': True, 'sylow': 0}
    • id: 115726463
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '81.4', 'subgroup_hash': 4, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726464
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '81.4', 'subgroup_hash': 4, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726465
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 54, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '18.a1', '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': 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: 115726466
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.18.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': '18.3', '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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726467
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 54, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.18.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726468
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726469
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.18.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726471
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.18.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': '54.9', 'subgroup_hash': 9, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726472
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726473
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726474
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.18.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726475
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 27, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.18.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726476
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726477
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.27.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726478
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.27.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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726479
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.27.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726480
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.27.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726482
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 115726483
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.36.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': '36.12', '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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726484
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 27, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.36.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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726485
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.36.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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726486
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.36.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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726487
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.36.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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726488
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 46, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '972.655.54.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': '54.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_6', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726489
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 18, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.54.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': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726490
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.54.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726491
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 49, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.54.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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726493
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.54.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726494
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 51, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.54.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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726495
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 52, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.54.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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 115726496
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726497
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726498
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.54.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726499
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.54.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726500
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.54.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': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726501
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.81.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726502
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726504
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.81.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726505
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 61, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '972.655.108.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': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726506
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': True, 'core_order': 9, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.655.108.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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 115726507
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.108.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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 115726508
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 64, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.108.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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726509
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.108.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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 115726510
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 66, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.108.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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726511
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.108.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': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
    • id: 115726512
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 6, 'counter': 68, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '972.655.162.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': '162.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3.S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726513
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 6, 'counter': 69, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '972.655.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '162.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 162, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3.S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726515
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.162.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726516
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
    • id: 115726517
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726518
      {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.655.162.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.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': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726519
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '972.655.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.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': 243, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 2}
    • id: 115726520
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 75, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '972.655.324.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': '324.146', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 146, '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': ['C6'], '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: 115726521
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 486, 'characteristic': False, 'core_order': 3, 'counter': 76, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '972.655.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.147', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 147, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3.D_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: 115726522
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.324.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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
    • id: 115726523
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 2, 'counter': 78, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '972.655.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '486.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '486.154', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 154, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 486, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9^2:C_6', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
    • id: 115726524
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.655.486.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, '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: 115726526
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.655', 'ambient_counter': 655, 'ambient_order': 972, 'ambient_tex': 'C_2\\times C_9^2:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 1, 'counter': 80, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '972.655.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '972.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '972.655', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 655, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 972, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_9^2:C_6', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', '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 • Show schema
    • id: 115726448
      {'ambient': '972.655', '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': '486.a1', 'complements': ['972.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '3.a1', '3.b1', '3.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4924, 2296, 5217, 2925], 'generators': [3, 18, 756, 486, 324, 2, 42], 'label': '972.655.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '486.154', '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': '486.154'}
    • id: 115726449
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '648.659', 'aut_weyl_index': 162, 'centralizer': '6.c1', 'complements': ['162.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.c1', '18.b1', '18.c1'], 'core': '6.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4557, 2764, 3681, 1970], 'generators': [486, 324, 6, 108, 18], 'label': '972.655.6.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1', 'normal_contained_in': ['2.a1', '3.a1'], 'normal_contains': ['12.c1', '18.b1', '18.c1'], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': '486.154', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 115726450
      {'ambient': '972.655', 'aut_centralizer_order': 1, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '486.a1', 'complements': ['162.c1', '162.d1'], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.c1', '18.i1', '18.j1'], 'core': '6.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [5073, 1098, 4831, 442], 'generators': [3, 324, 42, 756, 18], 'label': '972.655.6.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.d1', 'normal_contained_in': ['2.b1', '3.a1'], 'normal_contains': ['12.c1'], 'normalizer': '1.a1', 'old_label': '6.d1', 'projective_image': '972.655', 'quotient_action_image': '3.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '486.154'}
    • id: 115726451
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '162.52', 'aut_weyl_index': 648, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['12.d1', '18.b1', '18.e1', '18.f1'], 'core': '18.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3741, -1, 1673, -1], 'generators': [486, 324, 110, 6, 18], 'label': '972.655.6.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '6.e1', 'projective_image': '486.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1', 'subgroup_fusion': None, 'weyl_group': '27.5'}
    • id: 115726452
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '162.52', 'aut_weyl_index': 648, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['12.e1', '18.c1', '18.e1', '18.f1'], 'core': '18.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [6436, -1, 1022, -1], 'generators': [486, 324, 14, 762, 18], 'label': '972.655.6.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': '486.154', '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': '27.5'}
    • id: 115726453
      {'ambient': '972.655', 'aut_centralizer_order': 9, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 108, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '3.b1'], 'contains': ['12.a1', '18.g1', '18.h1', '18.i1'], 'core': '12.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2900, -1, 6485, -1], 'generators': [3, 18, 2, 42, 324], 'label': '972.655.6.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.g1', 'projective_image': '972.655', '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': '162.42'}
    • id: 115726454
      {'ambient': '972.655', 'aut_centralizer_order': 9, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 108, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '3.c1'], 'contains': ['12.b1', '18.h1', '18.j1'], 'core': '12.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8131, -1, 5252, -1], 'generators': [3, 342, 2, 798, 324], 'label': '972.655.6.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '6.h1', 'projective_image': '972.655', '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': '162.5'}
    • id: 115726455
      {'ambient': '972.655', 'aut_centralizer_order': 18, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '108.26', 'aut_weyl_index': 972, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['3.b1'], 'contains': ['18.d1', '18.g1', '27.a1', '27.c1'], 'core': '54.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [710, -1, 8454, -1], 'generators': [3, 18, 486, 2, 42], 'label': '972.655.9.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': '486.154', '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': '54.6'}
    • id: 115726456
      {'ambient': '972.655', 'aut_centralizer_order': 81, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 729, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1', '3.c1'], 'contains': ['18.a1', '18.h1', '27.a1', '27.b1', '27.d1'], 'core': '18.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5721, -1, 7803, -1], 'generators': [3, 324, 486, 2, 18], 'label': '972.655.9.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': '486.154', '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': '18.4'}
    • id: 115726457
      {'ambient': '972.655', 'aut_centralizer_order': 9, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 54, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1', '3.b1'], 'contains': ['18.b1', '18.i1', '27.c1', '27.d1'], 'core': '18.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1797, -1, 7151, -1], 'generators': [3, 18, 486, 42, 324], 'label': '972.655.9.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '9.c1', 'projective_image': '486.154', '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': '162.42'}
    • id: 115726458
      {'ambient': '972.655', 'aut_centralizer_order': 9, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 54, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1', '3.c1'], 'contains': ['18.c1', '18.j1', '27.d1', '27.e1'], 'core': '18.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [8835, -1, 5818, -1], 'generators': [3, 342, 486, 474, 324], 'label': '972.655.9.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '9.d1', 'projective_image': '486.154', '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': '162.5'}
    • id: 115726459
      {'ambient': '972.655', 'aut_centralizer_order': 18, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '5832.dk', 'aut_weyl_index': 18, 'centralizer': '54.b1', 'complements': ['486.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.a1', '6.b1', '6.c1', '6.e1', '6.f1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4924, 4662, 2995, 5099], 'generators': [486, 324, 18, 2, 6, 108], 'label': '972.655.2.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': '486.154', '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': '54.13'}
    • id: 115726460
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '324.167', 'aut_weyl_index': 324, 'centralizer': '54.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.a1', '6.g1'], 'contains': ['36.a1', '36.b1', '36.d1', '36.e1'], 'core': '12.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3121, 4585, 3685, 3940], 'generators': [2, 6, 324], 'label': '972.655.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.a1', '6.a1'], 'normal_contains': ['36.a1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '972.655', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '54.13'}
    • id: 115726461
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '12.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '324.167', 'aut_weyl_index': 324, 'centralizer': '54.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.b1', '6.h1'], 'contains': ['36.a1', '36.c1', '36.f1'], 'core': '12.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7813, 7107, 2180, 7558], 'generators': [2, 114], 'label': '972.655.12.b1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': ['4.a1', '6.b1'], 'normal_contains': ['36.a1', '36.c1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '972.655', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '54.13'}
    • id: 115726462
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '12.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '648.659', 'aut_weyl_index': 162, 'centralizer': '6.c1', 'complements': ['81.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.c1', '6.d1'], 'contains': ['36.b1', '36.c1'], 'core': '12.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4755, 1983, 2562, 501], 'generators': [6, 108], 'label': '972.655.12.c1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1', 'normal_contained_in': ['4.a1', '6.c1', '6.d1'], 'normal_contains': ['36.b1', '36.c1'], 'normalizer': '1.a1', 'old_label': '12.c1', 'projective_image': '972.655', 'quotient_action_image': '6.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 115726463
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '162.52', 'aut_weyl_index': 648, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.e1'], 'contains': ['36.b1', '36.e1', '36.f1'], 'core': '36.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4404, -1, 1143, -1], 'generators': [110, 6], 'label': '972.655.12.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': '972.655', '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': '27.5'}
    • id: 115726464
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '162.52', 'aut_weyl_index': 648, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.f1'], 'contains': ['36.c1', '36.e1', '36.f1'], 'core': '36.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [6634, -1, 144, -1], 'generators': [14, 114], 'label': '972.655.12.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': '972.655', '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': '27.5'}
    • id: 115726465
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '18.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 1458, 'centralizer': '18.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '6.b1', '9.b1'], 'contains': ['36.a1', '54.b1', '54.c1', '54.e1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5427, 9032, 4952, 9170], 'generators': [486, 2, 18, 324], 'label': '972.655.18.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.a1', 'normal_contained_in': ['6.a1', '6.b1'], 'normal_contains': ['36.a1', '54.b1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '486.154', 'quotient_action_image': '18.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 115726466
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '18.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2916, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.c1', '6.e1', '9.c1'], 'contains': ['36.b1', '54.a1', '54.b1'], 'core': '18.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [1793, 2828, 4328, 1970], 'generators': [486, 6, 324, 18], 'label': '972.655.18.b1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1', 'normal_contained_in': ['6.a1', '6.c1'], 'normal_contains': ['36.b1', '54.a1', '54.b1'], 'normalizer': '1.a1', 'old_label': '18.b1', 'projective_image': '486.154', 'quotient_action_image': '6.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 115726467
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2916, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '6.c1', '6.f1', '9.d1'], 'contains': ['36.c1', '54.b1', '54.f1'], 'core': '18.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [9190, 5950, 3041, 5910], 'generators': [486, 762, 324, 342], 'label': '972.655.18.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': '486.154', '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: 115726468
      {'ambient': '972.655', 'aut_centralizer_order': 324, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '18.3', 'aut_weyl_index': 5832, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.d1', '54.a1', '54.c1', '54.d1'], 'core': '54.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [300, -1, 6294, -1], 'generators': [486, 2, 6, 18], 'label': '972.655.18.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': '486.154', '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': '18.3'}
    • id: 115726469
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 5832, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '6.e1', '6.f1'], 'contains': ['36.e1', '54.b1', '54.d1'], 'core': '54.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3741, -1, 1642, -1], 'generators': [486, 8, 324, 18], 'label': '972.655.18.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '18.e1', 'projective_image': '486.154', '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': '9.2'}
    • id: 115726470
      {'ambient': '972.655', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '486.a1', 'complements': ['486.a1', '486.b1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.d1', '6.g1', '6.h1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [5656, 2296, 4629, 2925], 'generators': [3, 324, 18, 2, 42, 756], 'label': '972.655.2.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': '972.655', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '486.154'}
    • id: 115726471
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 5832, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.b1', '6.e1', '6.f1'], 'contains': ['36.f1', '54.b1', '54.g1'], 'core': '54.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7354, -1, 643, -1], 'generators': [486, 122, 324, 666], 'label': '972.655.18.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '18.f1', 'projective_image': '486.154', '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': '9.2'}
    • id: 115726472
      {'ambient': '972.655', 'aut_centralizer_order': 18, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 1944, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.g1', '9.a1'], 'contains': ['36.d1', '54.h1', '54.j1'], 'core': '108.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [972, -1, 8454, -1], 'generators': [3, 2, 42, 18], 'label': '972.655.18.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.g1', 'projective_image': '972.655', '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': '54.6'}
    • id: 115726473
      {'ambient': '972.655', 'aut_centralizer_order': 81, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 1458, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.g1', '6.h1', '9.b1'], 'contains': ['36.a1', '54.h1', '54.i1', '54.k1'], 'core': '36.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6078, -1, 7951, -1], 'generators': [3, 2, 18, 324], 'label': '972.655.18.h1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.h1', 'projective_image': '972.655', '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': '18.4'}
    • id: 115726474
      {'ambient': '972.655', 'aut_centralizer_order': 9, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 108, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.d1', '6.g1', '9.c1'], 'contains': ['36.b1', '54.j1', '54.k1'], 'core': '36.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2460, -1, 6800, -1], 'generators': [3, 42, 324, 18], 'label': '972.655.18.i1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.i1', 'projective_image': '972.655', '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': '162.42'}
    • id: 115726475
      {'ambient': '972.655', 'aut_centralizer_order': 9, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '972.429', 'aut_weyl_index': 108, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.d1', '6.h1', '9.d1'], 'contains': ['36.c1', '54.k1', '54.l1'], 'core': '36.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [8674, -1, 5440, -1], 'generators': [3, 798, 324, 342], 'label': '972.655.18.j1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '18.j1', 'projective_image': '972.655', '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': '162.5'}
    • id: 115726476
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8748, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.a1', '9.b1'], 'contains': ['54.c1', '54.h1', '81.a1', '81.b1'], 'core': '162.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4296, -1, 9772, -1], 'generators': [3, 486, 2, 18], 'label': '972.655.27.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': '486.154', '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': '6.1'}
    • id: 115726477
      {'ambient': '972.655', 'aut_centralizer_order': 81, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '24.14', 'aut_weyl_index': 4374, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.b1'], 'contains': ['54.e1', '54.i1', '81.a1', '81.c1'], 'core': '162.b1', 'coset_action_label': None, 'count': 54, 'diagramx': [8110, -1, 9246, -1], 'generators': [3, 486, 2, 342], 'label': '972.655.27.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '27.b1', 'projective_image': '486.154', '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': '6.1'}
    • id: 115726478
      {'ambient': '972.655', 'aut_centralizer_order': 18, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '108.26', 'aut_weyl_index': 972, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['9.a1', '9.c1'], 'contains': ['54.a1', '54.j1', '81.b1'], 'core': '54.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [1395, -1, 8809, -1], 'generators': [3, 486, 42, 18], 'label': '972.655.27.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '27.c1', 'projective_image': '486.154', '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': '54.6'}
    • id: 115726479
      {'ambient': '972.655', 'aut_centralizer_order': 81, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.186', 'aut_weyl_index': 729, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '9.c1', '9.d1'], 'contains': ['54.b1', '54.k1', '81.b1', '81.c1'], 'core': '54.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5362, -1, 7304, -1], 'generators': [3, 486, 18, 324], 'label': '972.655.27.d1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '27.d1', 'projective_image': '486.154', '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': '18.4'}
    • id: 115726480
      {'ambient': '972.655', 'aut_centralizer_order': 18, 'aut_label': '27.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '108.26', 'aut_weyl_index': 972, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.d1'], 'contains': ['54.f1', '54.l1', '81.c1'], 'core': '162.b1', 'coset_action_label': None, 'count': 54, 'diagramx': [9636, -1, 5795, -1], 'generators': [3, 486, 474, 342], 'label': '972.655.27.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '27.e1', 'projective_image': '486.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1', 'subgroup_fusion': None, 'weyl_group': '18.1'}
    • id: 115726481
      {'ambient': '972.655', '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': '486.a1', 'complements': ['324.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.c1', '6.d1', '9.c1', '9.d1'], 'core': '3.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4384, 968, 5217, 1134], 'generators': [3, 324, 18, 486, 42, 756], 'label': '972.655.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['6.c1', '6.d1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '486.154', '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': '486.154'}
    • id: 115726482
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '36.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '72.40', 'aut_weyl_index': 1458, 'centralizer': '18.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.b1', '18.a1', '18.h1'], 'contains': ['108.b1', '108.c1', '108.e1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6320, 7510, 4730, 7558], 'generators': [2, 18, 324], 'label': '972.655.36.a1', 'mobius_quo': 0, 'mobius_sub': 54, 'normal_closure': '36.a1', 'normal_contained_in': ['12.a1', '12.b1', '18.a1'], 'normal_contains': ['108.b1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '972.655', 'quotient_action_image': '18.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 115726483
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2916, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.c1', '12.d1', '18.b1', '18.i1'], 'contains': ['108.a1', '108.b1'], 'core': '36.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2662, 1879, 3088, 3009], 'generators': [6, 324], 'label': '972.655.36.b1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.b1', 'normal_contained_in': ['12.a1', '12.c1', '18.b1'], 'normal_contains': ['108.a1', '108.b1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '972.655', 'quotient_action_image': '6.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 115726484
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '36.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '36.12', 'aut_weyl_index': 2916, 'centralizer': '6.c1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.c1', '12.e1', '18.c1', '18.j1'], 'contains': ['108.b1', '108.f1'], 'core': '36.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8875, 4637, 2558, 4633], 'generators': [114, 324], 'label': '972.655.36.c1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.c1', 'normal_contained_in': ['12.b1', '12.c1', '18.c1'], 'normal_contains': ['108.b1'], 'normalizer': '1.a1', 'old_label': '36.c1', 'projective_image': '972.655', '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: 115726485
      {'ambient': '972.655', 'aut_centralizer_order': 324, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '18.3', 'aut_weyl_index': 5832, 'centralizer': '54.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.a1', '18.d1', '18.g1'], 'contains': ['108.a1', '108.c1', '108.d1'], 'core': '108.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [320, -1, 5350, -1], 'generators': [2, 6], 'label': '972.655.36.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': '972.655', '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': '18.3'}
    • id: 115726486
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 5832, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.d1', '12.e1', '18.e1'], 'contains': ['108.b1', '108.d1'], 'core': '108.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3516, -1, 2028, -1], 'generators': [8, 324], 'label': '972.655.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.e1', 'projective_image': '972.655', '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': '9.2'}
    • id: 115726487
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 5832, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1', '12.d1', '12.e1', '18.f1'], 'contains': ['108.b1', '108.g1'], 'core': '108.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [7145, -1, 1150, -1], 'generators': [116, 324], 'label': '972.655.36.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '36.f1', 'projective_image': '972.655', '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': '9.2'}
    • id: 115726488
      {'ambient': '972.655', 'aut_centralizer_order': 2916, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 17496, 'centralizer': '6.c1', 'complements': ['18.g1'], 'conjugacy_class_count': 6, 'contained_in': ['18.b1', '18.d1', '27.c1'], 'contains': ['108.a1', '162.a1'], 'core': '54.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1483, 3010, 5701, 1672], 'generators': [486, 6, 18], 'label': '972.655.54.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.a1', 'normal_contained_in': ['18.b1'], 'normal_contains': ['108.a1', '162.a1'], 'normalizer': '1.a1', 'old_label': '54.a1', 'projective_image': '486.154', 'quotient_action_image': '6.2', 'quotient_action_kernel': '9.1', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 115726489
      {'ambient': '972.655', 'aut_centralizer_order': 13122, 'aut_label': '54.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 13122, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.b1', '18.c1', '18.e1', '18.f1', '27.d1'], 'contains': ['108.b1', '162.a1', '162.b1'], 'core': '54.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5177, 5950, 3619, 6257], 'generators': [486, 18, 324], 'label': '972.655.54.b1', 'mobius_quo': -3, 'mobius_sub': 27, 'normal_closure': '54.b1', 'normal_contained_in': ['18.a1', '18.b1', '18.c1'], 'normal_contains': ['108.b1', '162.a1', '162.b1'], 'normalizer': '1.a1', 'old_label': '54.b1', 'projective_image': '486.154', '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: 115726490
      {'ambient': '972.655', 'aut_centralizer_order': 2916, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 17496, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '18.d1', '27.a1'], 'contains': ['108.c1', '162.a1', '162.c1'], 'core': '162.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3161, -1, 6668, -1], 'generators': [486, 2, 18], 'label': '972.655.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.c1', 'projective_image': '486.154', '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': '6.1'}
    • id: 115726491
      {'ambient': '972.655', 'aut_centralizer_order': 2916, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '3.1', 'aut_weyl_index': 34992, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.d1', '18.e1'], 'contains': ['108.d1', '162.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2521, -1, 4399, -1], 'generators': [486, 8, 18], 'label': '972.655.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '54.d1', 'projective_image': '486.154', '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': '3.1'}
    • id: 115726492
      {'ambient': '972.655', 'aut_centralizer_order': 9, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 54, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.g1', '9.a1', '9.b1', '9.c1'], 'core': '6.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2175, -1, 7035, -1], 'generators': [3, 18, 324, 486, 2, 42], 'label': '972.655.3.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': '486.154', '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': '162.42'}
    • id: 115726493
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8748, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.a1', '27.b1'], 'contains': ['108.e1', '162.b1', '162.c1'], 'core': '162.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7209, -1, 6138, -1], 'generators': [486, 2, 342], 'label': '972.655.54.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '54.e1', 'projective_image': '486.154', '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': '6.1'}
    • id: 115726494
      {'ambient': '972.655', 'aut_centralizer_order': 2916, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 17496, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '27.e1'], 'contains': ['108.f1', '162.b1'], 'core': '162.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9378, -1, 4055, -1], 'generators': [486, 798, 342], 'label': '972.655.54.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '54.f1', 'projective_image': '486.154', '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': '2.1'}
    • id: 115726495
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 17496, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.f1'], 'contains': ['108.g1', '162.b1'], 'core': '162.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8820, -1, 1591, -1], 'generators': [486, 122, 666], 'label': '972.655.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '54.g1', 'projective_image': '486.154', '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': '3.1'}
    • id: 115726496
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 17496, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.g1', '18.h1', '27.a1'], 'contains': ['108.c1', '162.d1', '162.e1'], 'core': '324.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4324, -1, 8926, -1], 'generators': [3, 2, 18], 'label': '972.655.54.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.h1', 'projective_image': '972.655', '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': '6.1'}
    • id: 115726497
      {'ambient': '972.655', 'aut_centralizer_order': 81, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8748, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.h1', '27.b1'], 'contains': ['108.e1', '162.d1', '162.f1'], 'core': '324.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [7757, -1, 8399, -1], 'generators': [3, 2, 342], 'label': '972.655.54.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '54.i1', 'projective_image': '972.655', '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': '6.1'}
    • id: 115726498
      {'ambient': '972.655', 'aut_centralizer_order': 18, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 1944, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['18.g1', '18.i1', '27.c1'], 'contains': ['108.a1', '162.e1'], 'core': '108.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1805, -1, 7713, -1], 'generators': [3, 42, 18], 'label': '972.655.54.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.j1', 'projective_image': '972.655', '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': '54.6'}
    • id: 115726499
      {'ambient': '972.655', 'aut_centralizer_order': 81, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '72.40', 'aut_weyl_index': 1458, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.h1', '18.i1', '18.j1', '27.d1'], 'contains': ['108.b1', '162.e1', '162.f1'], 'core': '108.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [5789, -1, 7112, -1], 'generators': [3, 18, 324], 'label': '972.655.54.k1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.k1', 'projective_image': '972.655', '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': '18.4'}
    • id: 115726500
      {'ambient': '972.655', 'aut_centralizer_order': 18, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '54.6', 'aut_weyl_index': 1944, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.j1', '27.e1'], 'contains': ['108.f1', '162.f1'], 'core': '324.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [9700, -1, 5030, -1], 'generators': [3, 798, 342], 'label': '972.655.54.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '54.l1', 'projective_image': '972.655', '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': '18.1'}
    • id: 115726501
      {'ambient': '972.655', 'aut_centralizer_order': 324, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 26244, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.b1'], 'contains': ['162.c1', '162.d1', '243.a1'], 'core': '486.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6521, -1, 9456, -1], 'generators': [3, 486, 2], 'label': '972.655.81.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '486.154', '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': '1.1'}
    • id: 115726502
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8748, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.a1', '27.c1', '27.d1'], 'contains': ['162.a1', '162.e1', '243.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3963, -1, 7994, -1], 'generators': [3, 486, 18], 'label': '972.655.81.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '81.b1', 'projective_image': '486.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 115726503
      {'ambient': '972.655', 'aut_centralizer_order': 9, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1944.2684', 'aut_weyl_index': 54, 'centralizer': '486.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['6.b1', '6.h1', '9.b1', '9.d1'], 'core': '6.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7503, -1, 5931, -1], 'generators': [3, 342, 324, 486, 2, 474], 'label': '972.655.3.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': '486.154', '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': '162.5'}
    • id: 115726504
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '81.c1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8748, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.b1', '27.d1', '27.e1'], 'contains': ['162.b1', '162.f1', '243.a1'], 'core': '162.b1', 'coset_action_label': None, 'count': 54, 'diagramx': [8183, -1, 7432, -1], 'generators': [3, 486, 342], 'label': '972.655.81.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '81.c1', 'projective_image': '486.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 115726505
      {'ambient': '972.655', 'aut_centralizer_order': 2916, 'aut_label': '108.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 17496, 'centralizer': '6.c1', 'complements': ['9.a1'], 'conjugacy_class_count': 6, 'contained_in': ['36.b1', '36.d1', '54.a1', '54.j1'], 'contains': ['324.a1'], 'core': '108.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1462, 3010, 5487, 3009], 'generators': [6], 'label': '972.655.108.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': ['36.b1', '54.a1'], 'normal_contains': ['324.a1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '972.655', 'quotient_action_image': '6.2', 'quotient_action_kernel': '18.2', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 115726506
      {'ambient': '972.655', 'aut_centralizer_order': 13122, 'aut_label': '108.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '8.3', 'aut_weyl_index': 13122, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.b1', '36.c1', '36.e1', '36.f1', '54.b1', '54.k1'], 'contains': ['324.a1', '324.b1'], 'core': '108.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5559, 4558, 3619, 5063], 'generators': [18, 324], 'label': '972.655.108.b1', 'mobius_quo': 3, 'mobius_sub': -54, 'normal_closure': '108.b1', 'normal_contained_in': ['36.a1', '36.b1', '36.c1', '54.b1'], 'normal_contains': ['324.a1', '324.b1'], 'normalizer': '1.a1', 'old_label': '108.b1', 'projective_image': '972.655', '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: 115726507
      {'ambient': '972.655', 'aut_centralizer_order': 2916, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 17496, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '36.d1', '54.c1', '54.h1'], 'contains': ['324.a1', '324.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3555, -1, 6387, -1], 'generators': [2, 18], 'label': '972.655.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '108.c1', 'projective_image': '972.655', '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': '6.1'}
    • id: 115726508
      {'ambient': '972.655', 'aut_centralizer_order': 2916, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '3.1', 'aut_weyl_index': 34992, 'centralizer': '18.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.d1', '36.e1', '54.d1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1752, -1, 4547, -1], 'generators': [8], 'label': '972.655.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '108.d1', 'projective_image': '972.655', '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': '3.1'}
    • id: 115726509
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 8748, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.a1', '54.e1', '54.i1'], 'contains': ['324.b1', '324.c1'], 'core': '324.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7101, -1, 6067, -1], 'generators': [2, 342], 'label': '972.655.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1', 'old_label': '108.e1', 'projective_image': '972.655', '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': '6.1'}
    • id: 115726510
      {'ambient': '972.655', 'aut_centralizer_order': 2916, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 17496, 'centralizer': '6.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.c1', '54.f1', '54.l1'], 'contains': ['324.b1'], 'core': '324.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9447, -1, 4087, -1], 'generators': [114], 'label': '972.655.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.f1', 'projective_image': '972.655', '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': '2.1'}
    • id: 115726511
      {'ambient': '972.655', 'aut_centralizer_order': 1458, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 17496, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.f1', '54.g1'], 'contains': ['324.b1'], 'core': '324.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8786, -1, 1591, -1], 'generators': [116], 'label': '972.655.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1', 'old_label': '108.g1', 'projective_image': '972.655', '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': '3.1'}
    • id: 115726512
      {'ambient': '972.655', 'aut_centralizer_order': 26244, 'aut_label': '162.a1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 52488, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '54.b1', '54.c1', '54.d1', '81.b1'], 'contains': ['324.a1', '486.a1'], 'core': '162.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3315, 4389, 5767, 4143], 'generators': [486, 18], 'label': '972.655.162.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '162.a1', 'normal_contained_in': ['54.a1', '54.b1'], 'normal_contains': ['324.a1', '486.a1'], 'normalizer': '1.a1', 'old_label': '162.a1', 'projective_image': '486.154', 'quotient_action_image': '2.1', 'quotient_action_kernel': '81.13', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 115726513
      {'ambient': '972.655', 'aut_centralizer_order': 26244, 'aut_label': '162.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 52488, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['54.b1', '54.e1', '54.f1', '54.g1', '81.c1'], 'contains': ['324.b1', '486.a1'], 'core': '162.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7970, 5820, 4976, 5982], 'generators': [486, 342], 'label': '972.655.162.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '162.b1', 'normal_contained_in': ['54.b1'], 'normal_contains': ['324.b1', '486.a1'], 'normalizer': '1.a1', 'old_label': '162.b1', 'projective_image': '486.154', 'quotient_action_image': '2.1', 'quotient_action_kernel': '81.14', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 115726514
      {'ambient': '972.655', 'aut_centralizer_order': 18, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '5832.dk', 'aut_weyl_index': 18, 'centralizer': '54.b1', 'complements': ['243.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1'], 'contains': ['12.a1', '12.b1', '12.c1', '12.d1', '12.e1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5488, 4571, 2328, 3869], 'generators': [2, 6, 108], 'label': '972.655.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['12.a1', '12.b1', '12.c1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '972.655', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '54.13'}
    • id: 115726515
      {'ambient': '972.655', 'aut_centralizer_order': 5832, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 52488, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1', '54.e1', '81.a1'], 'contains': ['324.c1', '486.a1'], 'core': '486.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4851, -1, 6968, -1], 'generators': [486, 2], 'label': '972.655.162.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '162.c1', 'projective_image': '486.154', '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': '1.1'}
    • id: 115726516
      {'ambient': '972.655', 'aut_centralizer_order': 324, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 52488, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.h1', '54.i1', '81.a1'], 'contains': ['324.c1', '486.b1'], 'core': '972.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [6408, -1, 8399, -1], 'generators': [3, 2], 'label': '972.655.162.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.d1', 'projective_image': '972.655', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 115726517
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 17496, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.h1', '54.j1', '54.k1', '81.b1'], 'contains': ['324.a1', '486.b1'], 'core': '324.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4284, -1, 7502, -1], 'generators': [3, 18], 'label': '972.655.162.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.e1', 'projective_image': '972.655', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 115726518
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 17496, 'centralizer': '162.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.i1', '54.k1', '54.l1', '81.c1'], 'contains': ['324.b1', '486.b1'], 'core': '324.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [8259, -1, 6687, -1], 'generators': [3, 342], 'label': '972.655.162.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1', 'old_label': '162.f1', 'projective_image': '972.655', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 115726519
      {'ambient': '972.655', 'aut_centralizer_order': 648, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 52488, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1', '81.c1'], 'contains': ['486.a1', '486.b1'], 'core': '486.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6743, -1, 7803, -1], 'generators': [3, 486], 'label': '972.655.243.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '243.a1', 'projective_image': '486.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 115726520
      {'ambient': '972.655', 'aut_centralizer_order': 26244, 'aut_label': '324.a1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 52488, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['108.a1', '108.b1', '108.c1', '108.d1', '162.a1', '162.e1'], 'contains': ['972.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3555, 3674, 5767, 4143], 'generators': [18], 'label': '972.655.324.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '324.a1', 'normal_contained_in': ['108.a1', '108.b1', '162.a1'], 'normal_contains': ['972.a1'], 'normalizer': '1.a1', 'old_label': '324.a1', 'projective_image': '972.655', 'quotient_action_image': '2.1', 'quotient_action_kernel': '162.49', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 115726521
      {'ambient': '972.655', 'aut_centralizer_order': 26244, 'aut_label': '324.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 52488, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['108.b1', '108.e1', '108.f1', '108.g1', '162.b1', '162.f1'], 'contains': ['972.a1'], 'core': '324.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8123, 5105, 4976, 5863], 'generators': [342], 'label': '972.655.324.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '324.b1', 'normal_contained_in': ['108.b1', '162.b1'], 'normal_contains': ['972.a1'], 'normalizer': '1.a1', 'old_label': '324.b1', 'projective_image': '972.655', 'quotient_action_image': '2.1', 'quotient_action_kernel': '162.50', 'quotient_action_kernel_order': 162, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 115726522
      {'ambient': '972.655', 'aut_centralizer_order': 5832, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 52488, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1', '108.e1', '162.c1', '162.d1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5607, -1, 6387, -1], 'generators': [2], 'label': '972.655.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '324.c1', 'projective_image': '972.655', '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: 115726523
      {'ambient': '972.655', 'aut_centralizer_order': 104976, 'aut_label': '486.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 104976, 'centralizer': '1.a1', 'complements': ['2.b1'], 'conjugacy_class_count': 1, 'contained_in': ['162.a1', '162.b1', '162.c1', '243.a1'], 'contains': ['972.a1'], 'core': '486.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6006, 4389, 6075, 5003], 'generators': [486], 'label': '972.655.486.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '486.a1', 'normal_contained_in': ['162.a1', '162.b1'], 'normal_contains': ['972.a1'], 'normalizer': '1.a1', 'old_label': '486.a1', 'projective_image': '486.154', 'quotient_action_image': '1.1', 'quotient_action_kernel': '486.154', 'quotient_action_kernel_order': 486, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 115726524
      {'ambient': '972.655', 'aut_centralizer_order': 648, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '1.1', 'aut_weyl_index': 104976, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['162.d1', '162.e1', '162.f1', '243.a1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [6525, -1, 7502, -1], 'generators': [3], 'label': '972.655.486.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.b1', 'projective_image': '972.655', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 115726525
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '324.167', 'aut_weyl_index': 324, 'centralizer': '54.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.b1'], 'contains': ['12.a1', '18.a1', '18.b1', '18.d1', '18.e1'], 'core': '6.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2211, 5897, 4324, 5791], 'generators': [486, 18, 2, 6, 324], 'label': '972.655.6.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': '486.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '54.13'}
    • id: 115726526
      {'ambient': '972.655', 'aut_centralizer_order': None, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.b1', '324.c1', '486.a1', '486.b1'], 'contains': [], 'core': '972.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6006, 4389, 6075, 5003], 'generators': [], 'label': '972.655.972.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '972.a1', 'normal_contained_in': ['324.a1', '324.b1', '486.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '972.a1', 'projective_image': '972.655', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 115726527
      {'ambient': '972.655', 'aut_centralizer_order': 162, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '324.167', 'aut_weyl_index': 324, 'centralizer': '54.b1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '3.c1'], 'contains': ['12.b1', '18.a1', '18.c1', '18.f1'], 'core': '6.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7503, 8693, 2995, 7916], 'generators': [486, 324, 2, 762, 666], 'label': '972.655.6.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['12.b1', '18.a1', '18.c1'], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': '486.154', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '54.13'}