Formats: - HTML - YAML - JSON - 2026-07-23T04:40:42.394644
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.36', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [8, 6, 2, 12, 4], 'aut_gens': [[1, 8, 48, 576, 1728], [1, 2072, 848, 2880, 576], [193, 8, 2640, 2304, 3456], [211, 200, 1104, 4608, 1728], [35, 2808, 736, 1152, 2880], [19, 1080, 3328, 2304, 4032]], 'aut_group': None, 'aut_hash': 2723700116397070647, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20736, 'aut_permdeg': 30, 'aut_perms': [115513788134559631174539843907449, 246376107945412010180588627151091, 928781260963292346460418979857, 86471026573643898895722259311798, 82071269063573290359901144422681], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 6, 2, 1], [2, 9, 1, 2], [2, 54, 2, 1], [2, 81, 1, 1], [3, 4, 2, 1], [3, 8, 1, 1], [3, 32, 2, 1], [4, 9, 2, 1], [4, 18, 1, 1], [4, 54, 4, 1], [4, 81, 2, 1], [4, 162, 1, 1], [4, 162, 2, 1], [6, 12, 2, 1], [6, 36, 2, 1], [6, 48, 2, 1], [6, 72, 1, 1], [6, 96, 2, 1], [6, 108, 2, 1], [8, 9, 2, 2], [8, 54, 4, 2], [8, 81, 2, 2], [8, 162, 2, 2], [12, 36, 4, 1], [12, 108, 4, 1], [12, 144, 1, 1], [24, 36, 4, 2], [24, 108, 4, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.C_4^2.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 2723700116397070647, 'autcentquo_nilpotent': False, 'autcentquo_order': 20736, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4.C_4^2.C_2^4', 'cc_stats': [[1, 1, 1], [2, 6, 2], [2, 9, 2], [2, 54, 2], [2, 81, 1], [3, 4, 2], [3, 8, 1], [3, 32, 2], [4, 9, 2], [4, 18, 1], [4, 54, 4], [4, 81, 2], [4, 162, 3], [6, 12, 2], [6, 36, 2], [6, 48, 2], [6, 72, 1], [6, 96, 2], [6, 108, 2], [8, 9, 4], [8, 54, 8], [8, 81, 4], [8, 162, 4], [12, 36, 4], [12, 108, 4], [12, 144, 1], [24, 36, 8], [24, 108, 8]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '5184.tb', 'commutator_count': 1, 'commutator_label': '162.52', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 496, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['72.39', 1], ['72.40', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 2], [2, 9, 1, 2], [2, 54, 1, 2], [2, 81, 1, 1], [3, 4, 1, 2], [3, 8, 1, 1], [3, 32, 1, 2], [4, 9, 2, 1], [4, 18, 1, 1], [4, 54, 2, 2], [4, 81, 2, 1], [4, 162, 1, 1], [4, 162, 2, 1], [6, 12, 1, 2], [6, 36, 1, 2], [6, 48, 1, 2], [6, 72, 1, 1], [6, 96, 1, 2], [6, 108, 1, 2], [8, 9, 4, 1], [8, 54, 4, 2], [8, 81, 4, 1], [8, 162, 4, 1], [12, 36, 2, 2], [12, 108, 2, 2], [12, 144, 1, 1], [24, 36, 4, 2], [24, 108, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2150400, 'exponent': 24, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[32, 1, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '5184.tb', 'hash': 4564102885012952942, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [8, 6, 12, 3, 3], 'inner_gens': [[1, 408, 256, 576, 1728], [225, 8, 912, 4608, 1728], [417, 872, 48, 4608, 2880], [1, 2888, 2928, 576, 1728], [1, 8, 624, 576, 1728]], 'inner_hash': 4564102885012952942, 'inner_nilpotent': False, 'inner_order': 5184, 'inner_split': False, 'inner_tex': 'F_9\\times \\SOPlus(4,2)', 'inner_used': [1, 2, 3], 'irrC_degree': 32, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 32, 'irrep_stats': [[1, 32], [2, 8], [4, 32], [8, 4], [16, 1], [32, 4]], 'label': '5184.tb', 'linC_count': 128, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 32, 'linQ_dim': 12, 'linQ_dim_count': 32, 'linR_count': 32, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'F9*SO+(4,2)', 'ngens': 10, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 81, 'number_divisions': 45, 'number_normal_subgroups': 56, 'number_subgroup_autclasses': 343, 'number_subgroup_classes': 551, 'number_subgroups': 18604, 'old_label': None, 'order': 5184, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 219], [3, 80], [4, 900], [6, 672], [8, 1440], [12, 720], [24, 1152]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [3888, 0], 'outer_gens': [[1, 4184, 4656, 4032, 1152], [3, 200, 240, 576, 1728]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 8], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 13], [8, 9], [16, 5], [32, 4]], 'representations': {'PC': {'code': '70381884164544638937682972067582636979154537191088978144511143312109244300603782804443498456244589214842496428911655', 'gens': [1, 4, 6, 9, 10], 'pres': [10, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 20, 51, 16323, 4013, 423, 113, 9604, 10014, 424, 15365, 8175, 3625, 6875, 175, 35846, 17376, 8426, 26076, 206, 32007, 16657, 7707, 51878, 8698, 1148, 6059, 3669]}, 'Perm': {'d': 15, 'gens': [219574, 287404906172, 338677, 105609, 368871477909, 45507, 268240959516, 19203650492, 267762193763, 224189]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 8], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'F_9\\times \\SOPlus(4,2)', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 163583664
      {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 496, 'group_order': 5184, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 163583675
      {'aut_label': '2A', 'centralizer': '6.a1.a1', 'counter': 2, 'group_counter': 496, 'group_order': 5184, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 24, 'size': 6}
    • id: 163583686
      {'aut_label': '2A', 'centralizer': '6.a1.b1', 'counter': 3, 'group_counter': 496, 'group_order': 5184, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1320, 'size': 6}
    • id: 163583697
      {'aut_label': '2C', 'centralizer': '9.b1.a1', 'counter': 4, 'group_counter': 496, 'group_order': 5184, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 4, 'size': 9}
    • id: 163583708
      {'aut_label': '2D', 'centralizer': '9.a1.a1', 'counter': 5, 'group_counter': 496, 'group_order': 5184, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 2592, 'size': 9}
    • id: 163583719
      {'aut_label': '2E', 'centralizer': '54.a1.b1', 'counter': 6, 'group_counter': 496, 'group_order': 5184, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 4316, 'size': 54}
    • id: 163583730
      {'aut_label': '2E', 'centralizer': '54.a1.a1', 'counter': 7, 'group_counter': 496, 'group_order': 5184, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 1084, 'size': 54}
    • id: 163583741
      {'aut_label': '2G', 'centralizer': '81.a1.a1', 'counter': 8, 'group_counter': 496, 'group_order': 5184, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 900, 'size': 81}
    • id: 163583744
      {'aut_label': '3A', 'centralizer': '4.i1.a1', 'counter': 9, 'group_counter': 496, 'group_order': 5184, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 3456, 'size': 4}
    • id: 163583665
      {'aut_label': '3A', 'centralizer': '4.i1.b1', 'counter': 10, 'group_counter': 496, 'group_order': 5184, 'label': '3B', 'order': 3, 'powers': [10, 1], 'representative': 1152, 'size': 4}
    • id: 163583666
      {'aut_label': '3C', 'centralizer': '8.c1.a1', 'counter': 11, 'group_counter': 496, 'group_order': 5184, 'label': '3C', 'order': 3, 'powers': [11, 1], 'representative': 16, 'size': 8}
    • id: 163583667
      {'aut_label': '3D', 'centralizer': '32.d1.b1', 'counter': 12, 'group_counter': 496, 'group_order': 5184, 'label': '3D', 'order': 3, 'powers': [12, 1], 'representative': 4832, 'size': 32}
    • id: 163583668
      {'aut_label': '3D', 'centralizer': '32.d1.a1', 'counter': 13, 'group_counter': 496, 'group_order': 5184, 'label': '3E', 'order': 3, 'powers': [13, 1], 'representative': 3472, 'size': 32}
    • id: 163583669
      {'aut_label': '4A1', 'centralizer': '9.b1.a1', 'counter': 14, 'group_counter': 496, 'group_order': 5184, 'label': '4A1', 'order': 4, 'powers': [4, 15], 'representative': 6, 'size': 9}
    • id: 163583670
      {'aut_label': '4A1', 'centralizer': '9.b1.a1', 'counter': 15, 'group_counter': 496, 'group_order': 5184, 'label': '4A-1', 'order': 4, 'powers': [4, 14], 'representative': 2, 'size': 9}
    • id: 163583671
      {'aut_label': '4B', 'centralizer': '18.i1.a1', 'counter': 16, 'group_counter': 496, 'group_order': 5184, 'label': '4B', 'order': 4, 'powers': [5, 16], 'representative': 3024, 'size': 18}
    • id: 163583672
      {'aut_label': '4C1', 'centralizer': '54.a1.a1', 'counter': 17, 'group_counter': 496, 'group_order': 5184, 'label': '4C1', 'order': 4, 'powers': [4, 18], 'representative': 30, 'size': 54}
    • id: 163583673
      {'aut_label': '4C1', 'centralizer': '54.a1.a1', 'counter': 18, 'group_counter': 496, 'group_order': 5184, 'label': '4C-1', 'order': 4, 'powers': [4, 17], 'representative': 26, 'size': 54}
    • id: 163583674
      {'aut_label': '4C1', 'centralizer': '54.a1.b1', 'counter': 19, 'group_counter': 496, 'group_order': 5184, 'label': '4D1', 'order': 4, 'powers': [4, 20], 'representative': 5054, 'size': 54}
    • id: 163583676
      {'aut_label': '4C1', 'centralizer': '54.a1.b1', 'counter': 20, 'group_counter': 496, 'group_order': 5184, 'label': '4D-1', 'order': 4, 'powers': [4, 19], 'representative': 4890, 'size': 54}
    • id: 163583677
      {'aut_label': '4E1', 'centralizer': '81.a1.a1', 'counter': 21, 'group_counter': 496, 'group_order': 5184, 'label': '4E1', 'order': 4, 'powers': [4, 22], 'representative': 3174, 'size': 81}
    • id: 163583678
      {'aut_label': '4E1', 'centralizer': '81.a1.a1', 'counter': 22, 'group_counter': 496, 'group_order': 5184, 'label': '4E-1', 'order': 4, 'powers': [4, 21], 'representative': 3170, 'size': 81}
    • id: 163583679
      {'aut_label': '4F', 'centralizer': '162.d1.a1', 'counter': 23, 'group_counter': 496, 'group_order': 5184, 'label': '4F', 'order': 4, 'powers': [5, 23], 'representative': 3892, 'size': 162}
    • id: 163583680
      {'aut_label': '4G1', 'centralizer': '162.d1.a1', 'counter': 24, 'group_counter': 496, 'group_order': 5184, 'label': '4G1', 'order': 4, 'powers': [8, 25], 'representative': 4310, 'size': 162}
    • id: 163583681
      {'aut_label': '4G1', 'centralizer': '162.d1.a1', 'counter': 25, 'group_counter': 496, 'group_order': 5184, 'label': '4G-1', 'order': 4, 'powers': [8, 24], 'representative': 2066, 'size': 162}
    • id: 163583682
      {'aut_label': '6A', 'centralizer': '12.a1.a1', 'counter': 26, 'group_counter': 496, 'group_order': 5184, 'label': '6A', 'order': 6, 'powers': [9, 2], 'representative': 1752, 'size': 12}
    • id: 163583683
      {'aut_label': '6A', 'centralizer': '12.a1.b1', 'counter': 27, 'group_counter': 496, 'group_order': 5184, 'label': '6B', 'order': 6, 'powers': [10, 3], 'representative': 168, 'size': 12}
    • id: 163583684
      {'aut_label': '6C', 'centralizer': '36.e1.a1', 'counter': 28, 'group_counter': 496, 'group_order': 5184, 'label': '6C', 'order': 6, 'powers': [9, 4], 'representative': 1732, 'size': 36}
    • id: 163583685
      {'aut_label': '6C', 'centralizer': '36.e1.b1', 'counter': 29, 'group_counter': 496, 'group_order': 5184, 'label': '6D', 'order': 6, 'powers': [10, 4], 'representative': 580, 'size': 36}
    • id: 163583687
      {'aut_label': '6E', 'centralizer': '48.h1.a1', 'counter': 30, 'group_counter': 496, 'group_order': 5184, 'label': '6E', 'order': 6, 'powers': [11, 2], 'representative': 8, 'size': 48}
    • id: 163583688
      {'aut_label': '6E', 'centralizer': '48.h1.b1', 'counter': 31, 'group_counter': 496, 'group_order': 5184, 'label': '6F', 'order': 6, 'powers': [11, 3], 'representative': 3512, 'size': 48}
    • id: 163583689
      {'aut_label': '6G', 'centralizer': '72.j1.a1', 'counter': 32, 'group_counter': 496, 'group_order': 5184, 'label': '6G', 'order': 6, 'powers': [11, 5], 'representative': 5120, 'size': 72}
    • id: 163583690
      {'aut_label': '6H', 'centralizer': '96.a1.b1', 'counter': 33, 'group_counter': 496, 'group_order': 5184, 'label': '6H', 'order': 6, 'powers': [12, 3], 'representative': 280, 'size': 96}
    • id: 163583691
      {'aut_label': '6H', 'centralizer': '96.a1.a1', 'counter': 34, 'group_counter': 496, 'group_order': 5184, 'label': '6I', 'order': 6, 'powers': [13, 2], 'representative': 1736, 'size': 96}
    • id: 163583692
      {'aut_label': '6J', 'centralizer': '108.a1.b1', 'counter': 35, 'group_counter': 496, 'group_order': 5184, 'label': '6J', 'order': 6, 'powers': [10, 6], 'representative': 2012, 'size': 108}
    • id: 163583693
      {'aut_label': '6J', 'centralizer': '108.a1.a1', 'counter': 36, 'group_counter': 496, 'group_order': 5184, 'label': '6K', 'order': 6, 'powers': [9, 7], 'representative': 5116, 'size': 108}
    • id: 163583694
      {'aut_label': '8A1', 'centralizer': '9.b1.a1', 'counter': 37, 'group_counter': 496, 'group_order': 5184, 'label': '8A1', 'order': 8, 'powers': [14, 39], 'representative': 3, 'size': 9}
    • id: 163583695
      {'aut_label': '8A-1', 'centralizer': '9.b1.a1', 'counter': 38, 'group_counter': 496, 'group_order': 5184, 'label': '8A-1', 'order': 8, 'powers': [15, 40], 'representative': 5, 'size': 9}
    • id: 163583696
      {'aut_label': '8A1', 'centralizer': '9.b1.a1', 'counter': 39, 'group_counter': 496, 'group_order': 5184, 'label': '8A3', 'order': 8, 'powers': [15, 37], 'representative': 1, 'size': 9}
    • id: 163583698
      {'aut_label': '8A-1', 'centralizer': '9.b1.a1', 'counter': 40, 'group_counter': 496, 'group_order': 5184, 'label': '8A-3', 'order': 8, 'powers': [14, 38], 'representative': 7, 'size': 9}
    • id: 163583699
      {'aut_label': '8B1', 'centralizer': '54.a1.a1', 'counter': 41, 'group_counter': 496, 'group_order': 5184, 'label': '8B1', 'order': 8, 'powers': [15, 43], 'representative': 233, 'size': 54}
    • id: 163583700
      {'aut_label': '8B-1', 'centralizer': '54.a1.a1', 'counter': 42, 'group_counter': 496, 'group_order': 5184, 'label': '8B-1', 'order': 8, 'powers': [14, 44], 'representative': 431, 'size': 54}
    • id: 163583701
      {'aut_label': '8B1', 'centralizer': '54.a1.a1', 'counter': 43, 'group_counter': 496, 'group_order': 5184, 'label': '8B3', 'order': 8, 'powers': [14, 41], 'representative': 395, 'size': 54}
    • id: 163583702
      {'aut_label': '8B-1', 'centralizer': '54.a1.a1', 'counter': 44, 'group_counter': 496, 'group_order': 5184, 'label': '8B-3', 'order': 8, 'powers': [15, 42], 'representative': 13, 'size': 54}
    • id: 163583703
      {'aut_label': '8B-1', 'centralizer': '54.a1.b1', 'counter': 45, 'group_counter': 496, 'group_order': 5184, 'label': '8C1', 'order': 8, 'powers': [14, 47], 'representative': 1311, 'size': 54}
    • id: 163583704
      {'aut_label': '8B1', 'centralizer': '54.a1.b1', 'counter': 46, 'group_counter': 496, 'group_order': 5184, 'label': '8C-1', 'order': 8, 'powers': [15, 48], 'representative': 1513, 'size': 54}
    • id: 163583705
      {'aut_label': '8B-1', 'centralizer': '54.a1.b1', 'counter': 47, 'group_counter': 496, 'group_order': 5184, 'label': '8C3', 'order': 8, 'powers': [15, 45], 'representative': 1501, 'size': 54}
    • id: 163583706
      {'aut_label': '8B1', 'centralizer': '54.a1.b1', 'counter': 48, 'group_counter': 496, 'group_order': 5184, 'label': '8C-3', 'order': 8, 'powers': [14, 46], 'representative': 1707, 'size': 54}
    • id: 163583707
      {'aut_label': '8D1', 'centralizer': '81.a1.a1', 'counter': 49, 'group_counter': 496, 'group_order': 5184, 'label': '8D1', 'order': 8, 'powers': [15, 51], 'representative': 705, 'size': 81}
    • id: 163583709
      {'aut_label': '8D-1', 'centralizer': '81.a1.a1', 'counter': 50, 'group_counter': 496, 'group_order': 5184, 'label': '8D-1', 'order': 8, 'powers': [14, 52], 'representative': 1095, 'size': 81}
    • id: 163583710
      {'aut_label': '8D1', 'centralizer': '81.a1.a1', 'counter': 51, 'group_counter': 496, 'group_order': 5184, 'label': '8D3', 'order': 8, 'powers': [14, 49], 'representative': 1075, 'size': 81}
    • id: 163583711
      {'aut_label': '8D-1', 'centralizer': '81.a1.a1', 'counter': 52, 'group_counter': 496, 'group_order': 5184, 'label': '8D-3', 'order': 8, 'powers': [15, 50], 'representative': 885, 'size': 81}
    • id: 163583712
      {'aut_label': '8E1', 'centralizer': '162.d1.a1', 'counter': 53, 'group_counter': 496, 'group_order': 5184, 'label': '8E1', 'order': 8, 'powers': [21, 55], 'representative': 723, 'size': 162}
    • id: 163583713
      {'aut_label': '8E-1', 'centralizer': '162.d1.a1', 'counter': 54, 'group_counter': 496, 'group_order': 5184, 'label': '8E-1', 'order': 8, 'powers': [22, 56], 'representative': 2741, 'size': 162}
    • id: 163583714
      {'aut_label': '8E1', 'centralizer': '162.d1.a1', 'counter': 55, 'group_counter': 496, 'group_order': 5184, 'label': '8E3', 'order': 8, 'powers': [22, 53], 'representative': 2737, 'size': 162}
    • id: 163583715
      {'aut_label': '8E-1', 'centralizer': '162.d1.a1', 'counter': 56, 'group_counter': 496, 'group_order': 5184, 'label': '8E-3', 'order': 8, 'powers': [21, 54], 'representative': 727, 'size': 162}
    • id: 163583716
      {'aut_label': '12A1', 'centralizer': '36.e1.a1', 'counter': 57, 'group_counter': 496, 'group_order': 5184, 'label': '12A1', 'order': 12, 'powers': [28, 14], 'representative': 3458, 'size': 36}
    • id: 163583717
      {'aut_label': '12A1', 'centralizer': '36.e1.a1', 'counter': 58, 'group_counter': 496, 'group_order': 5184, 'label': '12A-1', 'order': 12, 'powers': [28, 15], 'representative': 1734, 'size': 36}
    • id: 163583718
      {'aut_label': '12A1', 'centralizer': '36.e1.b1', 'counter': 59, 'group_counter': 496, 'group_order': 5184, 'label': '12B1', 'order': 12, 'powers': [29, 14], 'representative': 1154, 'size': 36}
    • id: 163583720
      {'aut_label': '12A1', 'centralizer': '36.e1.b1', 'counter': 60, 'group_counter': 496, 'group_order': 5184, 'label': '12B-1', 'order': 12, 'powers': [29, 15], 'representative': 582, 'size': 36}
    • id: 163583721
      {'aut_label': '12C1', 'centralizer': '108.a1.a1', 'counter': 61, 'group_counter': 496, 'group_order': 5184, 'label': '12C1', 'order': 12, 'powers': [28, 17], 'representative': 3482, 'size': 108}
    • id: 163583722
      {'aut_label': '12C1', 'centralizer': '108.a1.a1', 'counter': 62, 'group_counter': 496, 'group_order': 5184, 'label': '12C-1', 'order': 12, 'powers': [28, 18], 'representative': 1758, 'size': 108}
    • id: 163583723
      {'aut_label': '12C1', 'centralizer': '108.a1.b1', 'counter': 63, 'group_counter': 496, 'group_order': 5184, 'label': '12D1', 'order': 12, 'powers': [29, 19], 'representative': 282, 'size': 108}
    • id: 163583724
      {'aut_label': '12C1', 'centralizer': '108.a1.b1', 'counter': 64, 'group_counter': 496, 'group_order': 5184, 'label': '12D-1', 'order': 12, 'powers': [29, 20], 'representative': 2750, 'size': 108}
    • id: 163583725
      {'aut_label': '12E', 'centralizer': '144.y1.a1', 'counter': 65, 'group_counter': 496, 'group_order': 5184, 'label': '12E', 'order': 12, 'powers': [32, 16], 'representative': 1984, 'size': 144}
    • id: 163583726
      {'aut_label': '24A1', 'centralizer': '36.e1.a1', 'counter': 66, 'group_counter': 496, 'group_order': 5184, 'label': '24A1', 'order': 24, 'powers': [57, 37], 'representative': 1729, 'size': 36}
    • id: 163583727
      {'aut_label': '24A-1', 'centralizer': '36.e1.a1', 'counter': 67, 'group_counter': 496, 'group_order': 5184, 'label': '24A-1', 'order': 24, 'powers': [58, 38], 'representative': 1735, 'size': 36}
    • id: 163583728
      {'aut_label': '24A-1', 'centralizer': '36.e1.a1', 'counter': 68, 'group_counter': 496, 'group_order': 5184, 'label': '24A5', 'order': 24, 'powers': [57, 40], 'representative': 1733, 'size': 36}
    • id: 163583729
      {'aut_label': '24A1', 'centralizer': '36.e1.a1', 'counter': 69, 'group_counter': 496, 'group_order': 5184, 'label': '24A-5', 'order': 24, 'powers': [58, 39], 'representative': 1731, 'size': 36}
    • id: 163583731
      {'aut_label': '24A1', 'centralizer': '36.e1.b1', 'counter': 70, 'group_counter': 496, 'group_order': 5184, 'label': '24B1', 'order': 24, 'powers': [59, 37], 'representative': 577, 'size': 36}
    • id: 163583732
      {'aut_label': '24A-1', 'centralizer': '36.e1.b1', 'counter': 71, 'group_counter': 496, 'group_order': 5184, 'label': '24B-1', 'order': 24, 'powers': [60, 38], 'representative': 583, 'size': 36}
    • id: 163583733
      {'aut_label': '24A-1', 'centralizer': '36.e1.b1', 'counter': 72, 'group_counter': 496, 'group_order': 5184, 'label': '24B5', 'order': 24, 'powers': [59, 40], 'representative': 581, 'size': 36}
    • id: 163583734
      {'aut_label': '24A1', 'centralizer': '36.e1.b1', 'counter': 73, 'group_counter': 496, 'group_order': 5184, 'label': '24B-5', 'order': 24, 'powers': [60, 39], 'representative': 579, 'size': 36}
    • id: 163583735
      {'aut_label': '24C1', 'centralizer': '108.a1.a1', 'counter': 74, 'group_counter': 496, 'group_order': 5184, 'label': '24C1', 'order': 24, 'powers': [58, 41], 'representative': 2123, 'size': 108}
    • id: 163583736
      {'aut_label': '24C-1', 'centralizer': '108.a1.a1', 'counter': 75, 'group_counter': 496, 'group_order': 5184, 'label': '24C-1', 'order': 24, 'powers': [57, 42], 'representative': 3469, 'size': 108}
    • id: 163583737
      {'aut_label': '24C-1', 'centralizer': '108.a1.a1', 'counter': 76, 'group_counter': 496, 'group_order': 5184, 'label': '24C5', 'order': 24, 'powers': [58, 44], 'representative': 3887, 'size': 108}
    • id: 163583738
      {'aut_label': '24C1', 'centralizer': '108.a1.a1', 'counter': 77, 'group_counter': 496, 'group_order': 5184, 'label': '24C-5', 'order': 24, 'powers': [57, 43], 'representative': 1961, 'size': 108}
    • id: 163583739
      {'aut_label': '24C-1', 'centralizer': '108.a1.b1', 'counter': 78, 'group_counter': 496, 'group_order': 5184, 'label': '24D1', 'order': 24, 'powers': [59, 45], 'representative': 349, 'size': 108}
    • id: 163583740
      {'aut_label': '24C1', 'centralizer': '108.a1.b1', 'counter': 79, 'group_counter': 496, 'group_order': 5184, 'label': '24D-1', 'order': 24, 'powers': [60, 46], 'representative': 1131, 'size': 108}
    • id: 163583742
      {'aut_label': '24C1', 'centralizer': '108.a1.b1', 'counter': 80, 'group_counter': 496, 'group_order': 5184, 'label': '24D5', 'order': 24, 'powers': [59, 48], 'representative': 937, 'size': 108}
    • id: 163583743
      {'aut_label': '24C-1', 'centralizer': '108.a1.b1', 'counter': 81, 'group_counter': 496, 'group_order': 5184, 'label': '24D-5', 'order': 24, 'powers': [60, 47], 'representative': 159, 'size': 108}
  • gps_qchar • Show schema
    • id: 16335459
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 16335470
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 16335481
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 16335492
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 16335499
      {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 16335500
      {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 16335501
      {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 16335502
      {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 16335503
      {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1i', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, 2, 2, -2, -2, 2, -2, -2, -2, -2, 2, 2, -2, -2, 2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335460
      {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1j', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, 2, 2, -2, 2, 2, 2, 2, 2, 2, -2, -2, -2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, 2, 2, 2, -2, 2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 2, 2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335461
      {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1k', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, 2, 2, -2, 2, 2, 2, -2, 2, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335462
      {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1l', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335467
      {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 0, 0, 2, -2, 0, 0, -2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335468
      {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 0, 0, 2, -2, 0, 0, -2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335463
      {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1m', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, -4, -4, 4, 4, 4, -4, 4, 4, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, -4, -4, -4, -4, -4, -4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335464
      {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1n', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, -4, 4, -4, 4, 4, 4, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, -4, 4, -4, -4, -4, 4, 4, 4, -4, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335465
      {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1o', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, -4, -4, 4, 4, 4, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, -4, -4, -4, 4, -4, 4, -4, 4, 4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335466
      {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.1p', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, 4, -4, 4, -4, -4, -4, 4, 4, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 4, -4, -4, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335469
      {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.2c', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 0, 0, 4, -4, 0, 0, -4, 4, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 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: 16335472
      {'cdim': 4, 'counter': 21, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4a', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 0, 2, 4, 0, 2, 0, 0, -2, 1, 4, 1, -2, 4, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -1, -2, 1, 0, 2, 0, -1, 0, -1, 0, 4, 4, 4, 4, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, -1, -1, 0, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
    • id: 16335473
      {'cdim': 4, 'counter': 22, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4b', 'multiplicity': 1, 'nt': [6, 13], 'qdim': 4, 'qvalues': [4, 2, 0, 4, 0, 0, 2, 0, 1, -2, 4, -2, 1, 4, 4, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -2, 2, 0, 0, 0, -1, 0, -1, 4, 4, 4, 4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, -2, -1, -1, 0, 0, 0, 1, 1, 1, 1, -2, -2, -2, -2, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335474
      {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4c', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, -2, 0, 4, 0, 0, -2, 0, 1, -2, 4, -2, 1, 4, 4, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, -2, 0, 0, 0, 1, 0, 1, 4, 4, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, -2, 1, 1, 0, 0, 0, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335475
      {'cdim': 4, 'counter': 24, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4d', 'multiplicity': 1, 'nt': [12, 34], 'qdim': 4, 'qvalues': [4, 0, -2, 4, 0, -2, 0, 0, -2, 1, 4, 1, -2, 4, 4, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, -2, 0, 1, 0, 1, 0, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, 1, 1, 0, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
    • id: 16335476
      {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4e', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, -2, 0, 4, 0, 0, -2, 0, 1, -2, 4, -2, 1, 4, 4, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -2, -2, 0, 0, 0, 1, 0, 1, -4, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, -2, 1, 1, 0, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335477
      {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4f', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, 0, -2, 4, 0, -2, 0, 0, -2, 1, 4, 1, -2, 4, 4, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 1, -2, 1, 0, -2, 0, 1, 0, 1, 0, -4, -4, -4, -4, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, 1, 1, 0, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
    • id: 16335478
      {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4g', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, 0, 2, 4, 0, 2, 0, 0, -2, 1, 4, 1, -2, 4, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, -1, -2, 1, 0, 2, 0, -1, 0, -1, 0, -4, -4, -4, -4, 0, 0, 0, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 0, 0, -1, -1, 0, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
    • id: 16335479
      {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4h', 'multiplicity': 1, 'nt': [12, 77], 'qdim': 4, 'qvalues': [4, 2, 0, 4, 0, 0, 2, 0, 1, -2, 4, -2, 1, 4, 4, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, -2, 2, 0, 0, 0, -1, 0, -1, -4, -4, -4, -4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, -2, -1, -1, 0, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335471
      {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.2d', 'multiplicity': 4, 'nt': [16, 16], 'qdim': 8, 'qvalues': [8, 0, 0, -8, -8, 0, 0, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335480
      {'cdim': 4, 'counter': 29, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4i', 'multiplicity': 2, 'nt': [24, 643], 'qdim': 8, 'qvalues': [8, -4, 0, 8, 0, 0, -4, 0, 2, -4, 8, -4, 2, -8, -8, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -4, -4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335482
      {'cdim': 4, 'counter': 30, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4j', 'multiplicity': 2, 'nt': [24, 643], 'qdim': 8, 'qvalues': [8, 0, -4, 8, 0, -4, 0, 0, -4, 2, 8, 2, -4, -8, -8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 2, -4, 2, 0, -4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335483
      {'cdim': 4, 'counter': 31, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4k', 'multiplicity': 2, 'nt': [24, 643], 'qdim': 8, 'qvalues': [8, 0, 4, 8, 0, 4, 0, 0, -4, 2, 8, 2, -4, -8, -8, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, -2, -4, 2, 0, 4, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335484
      {'cdim': 4, 'counter': 32, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4l', 'multiplicity': 2, 'nt': [24, 643], 'qdim': 8, 'qvalues': [8, 4, 0, 8, 0, 0, 4, 0, 2, -4, 8, -4, 2, -8, -8, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, -2, 0, 2, -4, 4, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335489
      {'cdim': 8, 'counter': 37, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.8a', 'multiplicity': 1, 'nt': [9, 15], 'qdim': 8, 'qvalues': [8, 8, 8, 0, 8, 0, 0, 0, 8, 8, -1, -1, -1, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335490
      {'cdim': 8, 'counter': 38, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.8b', 'multiplicity': 1, 'nt': [18, 59], 'qdim': 8, 'qvalues': [8, -8, -8, 0, 8, 0, 0, 0, 8, 8, -1, -1, -1, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, 1, 1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335491
      {'cdim': 8, 'counter': 39, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.8c', 'multiplicity': 1, 'nt': [18, 59], 'qdim': 8, 'qvalues': [8, -8, 8, 0, 8, 0, 0, 0, 8, 8, -1, -1, -1, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335493
      {'cdim': 8, 'counter': 40, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.8d', 'multiplicity': 1, 'nt': [18, 59], 'qdim': 8, 'qvalues': [8, 8, -8, 0, 8, 0, 0, 0, 8, 8, -1, -1, -1, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335485
      {'cdim': 4, 'counter': 33, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4m', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -8, 0, -16, 0, 0, 8, 0, 4, -8, 16, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 8, -8, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 16335486
      {'cdim': 4, 'counter': 34, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4n', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, -8, -16, 0, 8, 0, 0, -8, 4, 16, 4, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, -4, 0, -8, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335487
      {'cdim': 4, 'counter': 35, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4o', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 0, 8, -16, 0, -8, 0, 0, -8, 4, 16, 4, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 8, -4, 0, 8, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335488
      {'cdim': 4, 'counter': 36, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.4p', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, 8, 0, -16, 0, 0, -8, 0, 4, -8, 16, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -4, 8, 8, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 16335494
      {'cdim': 16, 'counter': 41, 'faithful': False, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.16a', 'multiplicity': 1, 'nt': [36, 872], 'qdim': 16, 'qvalues': [16, 0, 0, 0, -16, 0, 0, 0, 16, 16, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 16335495
      {'cdim': 32, 'counter': 42, 'faithful': True, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.32a', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 0, 16, 0, 0, 0, 0, 0, -16, 8, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335496
      {'cdim': 32, 'counter': 43, 'faithful': True, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.32b', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 32, 'qvalues': [32, 16, 0, 0, 0, 0, 0, 0, 8, -16, -4, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335497
      {'cdim': 32, 'counter': 44, 'faithful': True, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.32c', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 32, 'qvalues': [32, -16, 0, 0, 0, 0, 0, 0, 8, -16, -4, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 16335498
      {'cdim': 32, 'counter': 45, 'faithful': True, 'group': '5184.tb', 'group_order': 5184, 'image': None, 'label': '5184.tb.32d', 'multiplicity': 1, 'nt': [96, 0], 'qdim': 32, 'qvalues': [32, 0, -16, 0, 0, 0, 0, 0, -16, 8, -4, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
    • id: 36458727
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 5184, 'label': '5184.tb.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 36458738
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    • id: 36458749
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    • id: 36458760
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 2592, 'label': '5184.tb.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 36458771
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 2592, 'label': '5184.tb.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 36458782
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 2592, 'label': '5184.tb.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 36458793
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 2592, 'label': '5184.tb.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 36458804
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 2592, 'label': '5184.tb.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 36458807
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 9, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.h1.a1', 'kernel_order': 1296, 'label': '5184.tb.1i1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
    • id: 36458728
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 10, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.h1.a1', 'kernel_order': 1296, 'label': '5184.tb.1i2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
    • id: 36458729
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 11, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 1296, 'label': '5184.tb.1j1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
    • id: 36458730
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 12, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 1296, 'label': '5184.tb.1j2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
    • id: 36458731
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 13, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 1296, 'label': '5184.tb.1k1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
    • id: 36458732
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    • id: 36458733
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    • id: 36458734
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    • id: 36458735
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 17, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.j1.a1', 'kernel_order': 648, 'label': '5184.tb.1m1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]]]}
    • id: 36458736
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 18, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.j1.a1', 'kernel_order': 648, 'label': '5184.tb.1m2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]]]}
    • id: 36458737
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 19, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.j1.a1', 'kernel_order': 648, 'label': '5184.tb.1m3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]]]}
    • id: 36458739
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 20, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.j1.a1', 'kernel_order': 648, 'label': '5184.tb.1m4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]]]}
    • id: 36458740
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 21, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.b1', 'kernel_order': 648, 'label': '5184.tb.1n1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]]]}
    • id: 36458741
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 22, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.b1', 'kernel_order': 648, 'label': '5184.tb.1n2', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]]]}
    • id: 36458742
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 23, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.b1', 'kernel_order': 648, 'label': '5184.tb.1n3', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]]]}
    • id: 36458743
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 24, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.b1', 'kernel_order': 648, 'label': '5184.tb.1n4', 'nt': [8, 4], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[-1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]]]}
    • id: 36458744
      {'center': '1.a1.a1', 'center_index': 1, 'center_order': 5184, 'counter': 25, 'cyclotomic_n': 8, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '8.1', 'image_order': 8, 'indicator': 0, 'kernel': '8.b1.a1', 'kernel_order': 648, 'label': '5184.tb.1o1', 'nt': [8, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[-1, 2]], [[1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[1, 0]], [[1, 2]], [[-1, 2]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 3]], [[-1, 1]], [[1, 1]], [[-1, 3]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-1, 1]], [[1, 3]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[1, 2]], [[-1, 2]], [[-1, 2]], [[1, 2]], [[-1, 0]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]]]}
    • id: 36458745
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    • id: 36458746
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    • id: 36458747
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    • id: 36458748
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    • id: 36458750
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    • id: 36458751
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    • id: 36458752
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    • id: 36458753
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    • id: 36458754
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    • id: 36458755
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    • id: 36458756
      {'center': '4.e1.a1', 'center_index': 4, 'center_order': 1296, 'counter': 36, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.a1', 'kernel_order': 324, 'label': '5184.tb.2c2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458757
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    • id: 36458758
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    • id: 36458759
      {'center': '4.e1.a1', 'center_index': 4, 'center_order': 1296, 'counter': 39, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 162, 'label': '5184.tb.2d3', 'nt': [16, 16], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458761
      {'center': '4.e1.a1', 'center_index': 4, 'center_order': 1296, 'counter': 40, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '32.38', 'image_order': 32, 'indicator': 0, 'kernel': '32.c1.a1', 'kernel_order': 162, 'label': '5184.tb.2d4', 'nt': [16, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 1]], [[-2, 3]], [[2, 1]], [[2, 3]], [[-2, 1]], [[-2, 3]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458762
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 41, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1.a1', 'kernel_order': 72, 'label': '5184.tb.4a', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 36458763
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 42, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1.a1', 'kernel_order': 72, 'label': '5184.tb.4b', 'nt': [6, 13], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458764
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1.a1', 'kernel_order': 72, 'label': '5184.tb.4c', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458765
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 44, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '72.40', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1.a1', 'kernel_order': 72, 'label': '5184.tb.4d', 'nt': [12, 34], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 36458766
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 45, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 36, 'label': '5184.tb.4e', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458767
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 46, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 36, 'label': '5184.tb.4f', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 36458768
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 47, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 36, 'label': '5184.tb.4g', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 36458769
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 48, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '144.186', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 36, 'label': '5184.tb.4h', 'nt': [12, 77], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458770
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 49, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '288.877', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 18, 'label': '5184.tb.4i1', 'nt': [24, 643], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-4, 1]], [[4, 1]], [[4, 1]], [[-4, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458772
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    • id: 36458773
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    • id: 36458774
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    • id: 36458775
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 53, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '288.877', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 18, 'label': '5184.tb.4k1', 'nt': [24, 643], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 1]], [[4, 1]], [[4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
    • id: 36458776
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    • id: 36458777
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 55, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '288.877', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 18, 'label': '5184.tb.4l1', 'nt': [24, 643], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-4, 1]], [[4, 1]], [[4, 1]], [[-4, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458778
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 56, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '288.877', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 18, 'label': '5184.tb.4l2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[4, 1]], [[-4, 1]], [[-4, 1]], [[4, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[2, 1]], [[-2, 1]], [[2, 1]], [[-2, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458779
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 57, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4m1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[4, 3]], [[-4, 1]], [[4, 1]], [[-4, 3]], [[-2, 1]], [[2, 3]], [[-2, 3]], [[2, 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]], [[1, 2]], [[-1, 2]], [[-2, 2]], [[2, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458780
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 58, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4m2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 2]], [[-4, 2]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-4, 1]], [[4, 3]], [[-4, 3]], [[4, 1]], [[2, 3]], [[-2, 1]], [[2, 1]], [[-2, 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]], [[-1, 2]], [[1, 2]], [[2, 2]], [[-2, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[2, 3]], [[-2, 1]], [[-2, 3]], [[2, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458781
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 59, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4m3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-4, 3]], [[4, 1]], [[-4, 1]], [[4, 3]], [[2, 1]], [[-2, 3]], [[2, 3]], [[-2, 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]], [[1, 2]], [[-1, 2]], [[-2, 2]], [[2, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[2, 1]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458783
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 60, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4m4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 2]], [[-4, 2]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[4, 1]], [[-4, 3]], [[4, 3]], [[-4, 1]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[2, 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]], [[-1, 2]], [[1, 2]], [[2, 2]], [[-2, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-2, 3]], [[2, 1]], [[2, 3]], [[-2, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458784
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 61, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4n1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 3]], [[-4, 1]], [[4, 1]], [[-4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 1]], [[2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 2]], [[0, 0]], [[-2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]]]}
    • id: 36458785
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    • id: 36458786
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 63, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4n3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-4, 3]], [[4, 1]], [[-4, 1]], [[4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 2]], [[0, 0]], [[2, 1]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]]]}
    • id: 36458787
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 64, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4n4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[-2, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 2]], [[-4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[4, 1]], [[-4, 3]], [[4, 3]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 2]], [[0, 0]], [[-2, 3]], [[2, 1]], [[2, 3]], [[-2, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]]]}
    • id: 36458788
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 65, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4o1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 3]], [[-4, 1]], [[4, 1]], [[-4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 2]], [[0, 0]], [[-2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]]]}
    • id: 36458789
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 66, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4o2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 2]], [[-4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, 1]], [[4, 3]], [[-4, 3]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 3]], [[2, 3]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 2]], [[0, 0]], [[2, 3]], [[-2, 1]], [[-2, 3]], [[2, 1]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]]]}
    • id: 36458790
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 67, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4o3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-4, 3]], [[4, 1]], [[-4, 1]], [[4, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 1]], [[2, 1]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[-1, 2]], [[1, 2]], [[0, 0]], [[2, 1]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]]]}
    • id: 36458791
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 68, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4o4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[4, 2]], [[-4, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[4, 1]], [[-4, 3]], [[4, 3]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 3]], [[-2, 3]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[1, 2]], [[-1, 2]], [[0, 0]], [[-2, 3]], [[2, 1]], [[2, 3]], [[-2, 1]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]]]}
    • id: 36458792
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 69, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4p1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[4, 3]], [[-4, 1]], [[4, 1]], [[-4, 3]], [[2, 1]], [[-2, 3]], [[2, 3]], [[-2, 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]], [[1, 2]], [[-1, 2]], [[-2, 2]], [[2, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[-2, 1]], [[2, 3]], [[2, 1]], [[-2, 3]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458794
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 70, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4p2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 2]], [[-4, 2]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-4, 1]], [[4, 3]], [[-4, 3]], [[4, 1]], [[-2, 3]], [[2, 1]], [[-2, 1]], [[2, 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]], [[-1, 2]], [[1, 2]], [[2, 2]], [[-2, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 1]], [[1, 3]], [[-1, 1]], [[2, 3]], [[-2, 1]], [[-2, 3]], [[2, 1]], [[1, 1]], [[-1, 3]], [[-1, 1]], [[1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458795
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 71, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4p3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-4, 2]], [[4, 2]], [[0, 0]], [[-2, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-4, 3]], [[4, 1]], [[-4, 1]], [[4, 3]], [[-2, 1]], [[2, 3]], [[-2, 3]], [[2, 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]], [[1, 2]], [[-1, 2]], [[-2, 2]], [[2, 2]], [[-1, 2]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[2, 1]], [[-2, 3]], [[-2, 1]], [[2, 3]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458796
      {'center': '72.b1.a1', 'center_index': 72, 'center_order': 72, 'counter': 72, 'cyclotomic_n': 8, 'dim': 4, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.5163', 'image_order': 576, 'indicator': 0, 'kernel': '576.b1.a1', 'kernel_order': 9, 'label': '5184.tb.4p4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[4, 2]], [[-4, 2]], [[0, 0]], [[2, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[4, 1]], [[-4, 3]], [[4, 3]], [[-4, 1]], [[2, 3]], [[-2, 1]], [[2, 1]], [[-2, 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]], [[-1, 2]], [[1, 2]], [[2, 2]], [[-2, 2]], [[1, 2]], [[-1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 1]], [[-1, 3]], [[1, 1]], [[-2, 3]], [[2, 1]], [[2, 3]], [[-2, 1]], [[-1, 1]], [[1, 3]], [[1, 1]], [[-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458797
      {'center': '72.a1.a1', 'center_index': 72, 'center_order': 72, 'counter': 73, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '72.39', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 72, 'label': '5184.tb.8a', 'nt': [9, 15], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458798
      {'center': '72.a1.a1', 'center_index': 72, 'center_order': 72, 'counter': 74, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '144.185', 'image_order': 144, 'indicator': 1, 'kernel': '144.c1.a1', 'kernel_order': 36, 'label': '5184.tb.8b', 'nt': [18, 59], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458799
      {'center': '72.a1.a1', 'center_index': 72, 'center_order': 72, 'counter': 75, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '144.185', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.b1', 'kernel_order': 36, 'label': '5184.tb.8c', 'nt': [18, 59], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458800
      {'center': '72.a1.a1', 'center_index': 72, 'center_order': 72, 'counter': 76, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '144.185', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 36, 'label': '5184.tb.8d', 'nt': [18, 59], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 36458801
      {'center': '288.b1.a1', 'center_index': 288, 'center_order': 18, 'counter': 77, 'cyclotomic_n': 1, 'dim': 16, 'faithful': False, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '576.8368', 'image_order': 576, 'indicator': 1, 'kernel': '576.a1.a1', 'kernel_order': 9, 'label': '5184.tb.16a', 'nt': [36, 872], 'q_character': None, 'values': [[[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[16, 0]], [[16, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 36458802
      {'center': '5184.a1.a1', 'center_index': 5184, 'center_order': 1, 'counter': 78, 'cyclotomic_n': 1, 'dim': 32, 'faithful': True, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '5184.tb', 'image_order': 5184, 'indicator': 1, 'kernel': '5184.a1.a1', 'kernel_order': 1, 'label': '5184.tb.32a', 'nt': [48, 0], 'q_character': None, 'values': [[[32, 0]], [[0, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[8, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 36458803
      {'center': '5184.a1.a1', 'center_index': 5184, 'center_order': 1, 'counter': 79, 'cyclotomic_n': 1, 'dim': 32, 'faithful': True, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '5184.tb', 'image_order': 5184, 'indicator': 1, 'kernel': '5184.a1.a1', 'kernel_order': 1, 'label': '5184.tb.32b', 'nt': [48, 0], 'q_character': None, 'values': [[[32, 0]], [[16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-16, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 36458805
      {'center': '5184.a1.a1', 'center_index': 5184, 'center_order': 1, 'counter': 80, 'cyclotomic_n': 1, 'dim': 32, 'faithful': True, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '5184.tb', 'image_order': 5184, 'indicator': 1, 'kernel': '5184.a1.a1', 'kernel_order': 1, 'label': '5184.tb.32c', 'nt': [96, 0], 'q_character': None, 'values': [[[32, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-16, 0]], [[-4, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 36458806
      {'center': '5184.a1.a1', 'center_index': 5184, 'center_order': 1, 'counter': 81, 'cyclotomic_n': 1, 'dim': 32, 'faithful': True, 'field': [0, 1], 'group': '5184.tb', 'group_counter': 496, 'group_order': 5184, 'image': None, 'image_isoclass': '5184.tb', 'image_order': 5184, 'indicator': 1, 'kernel': '5184.a1.a1', 'kernel_order': 1, 'label': '5184.tb.32d', 'nt': [96, 0], 'q_character': None, 'values': [[[32, 0]], [[0, 0]], [[-16, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-16, 0]], [[8, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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
    Showing the first 100 of 551 matching records in this table.
    • id: 223364789
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5184, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '5184.tb.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5184.tb', 'subgroup_hash': 4564102885012952942, 'subgroup_order': 5184, 'subgroup_tex': 'F_9\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
    • id: 223364900
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.nt', 'subgroup_hash': 412574259205366277, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^2\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365011
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.nt', 'subgroup_hash': 412574259205366277, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^2\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365122
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.fn', 'subgroup_hash': 7330864860993687166, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^2:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365233
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.fn', 'subgroup_hash': 7330864860993687166, 'subgroup_order': 2592, 'subgroup_tex': 'S_3^2:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365296
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2592, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2592.ft', 'subgroup_hash': 133552510359532722, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^4:(C_4\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 223365307
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2592, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.oy', 'subgroup_hash': 8171624199488353279, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^2:C_4\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365318
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 2592, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2592.pq', 'subgroup_hash': 6407552563315781201, 'subgroup_order': 2592, 'subgroup_tex': 'C_3^3:C_{12}:C_8', 'supersolvable': False, 'sylow': 0}
    • id: 223365329
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 223364790
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3524', 'subgroup_hash': 3524, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:C_4\\times S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 223364801
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
    • id: 223364812
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3498', 'subgroup_hash': 3498, 'subgroup_order': 1296, 'subgroup_tex': '(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
    • id: 223364823
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3527', 'subgroup_hash': 3527, 'subgroup_order': 1296, 'subgroup_tex': '(C_3\\times S_3^2):D_6', 'supersolvable': False, 'sylow': 0}
    • id: 223364834
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3496', 'subgroup_hash': 3496, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:C_4^2', 'supersolvable': False, 'sylow': 0}
    • id: 223364845
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3504', 'subgroup_hash': 3504, 'subgroup_order': 1296, 'subgroup_tex': 'C_3:S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223364856
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3505', 'subgroup_hash': 3505, 'subgroup_order': 1296, 'subgroup_tex': 'C_3:(S_3\\times F_9)', 'supersolvable': False, 'sylow': 0}
    • id: 223364867
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1296, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3505', 'subgroup_hash': 3505, 'subgroup_order': 1296, 'subgroup_tex': 'C_3:(S_3\\times F_9)', 'supersolvable': False, 'sylow': 0}
    • id: 223364878
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3507', 'subgroup_hash': 3507, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2:(C_2\\times F_9)', 'supersolvable': False, 'sylow': 0}
    • id: 223364889
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3500', 'subgroup_hash': 3500, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^2\\wr C_2.D_4', 'supersolvable': False, 'sylow': 0}
    • id: 223364901
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 648, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3502', 'subgroup_hash': 3502, 'subgroup_order': 1296, 'subgroup_tex': 'C_3\\times S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223364912
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 648, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3502', 'subgroup_hash': 3502, 'subgroup_order': 1296, 'subgroup_tex': 'C_3\\times S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223364923
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3503', 'subgroup_hash': 3503, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\times C_3:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223364934
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3503', 'subgroup_hash': 3503, 'subgroup_order': 1296, 'subgroup_tex': 'S_3\\times C_3:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223364945
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4681', 'subgroup_hash': 4681, 'subgroup_order': 864, 'subgroup_tex': 'D_6\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223364956
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '864.4681', 'subgroup_hash': 4681, 'subgroup_order': 864, 'subgroup_tex': 'D_6\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223364967
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 223364978
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.732', 'subgroup_hash': 732, 'subgroup_order': 648, 'subgroup_tex': 'C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 223364989
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365000
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.721', 'subgroup_hash': 721, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365012
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 648, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.718', 'subgroup_hash': 718, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365023
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 223365034
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.715', 'subgroup_hash': 715, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 223365045
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 223365056
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 648, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.716', 'subgroup_hash': 716, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 223365067
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.717', 'subgroup_hash': 717, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
    • id: 223365078
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 648, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.707', 'subgroup_hash': 707, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365089
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.709', 'subgroup_hash': 709, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365100
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.724', 'subgroup_hash': 724, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 223365111
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 223365123
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.8.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.713', 'subgroup_hash': 713, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 223365134
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
    • id: 223365145
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.714', 'subgroup_hash': 714, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
    • id: 223365156
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.708', 'subgroup_hash': 708, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_{24}', 'supersolvable': False, 'sylow': 0}
    • id: 223365167
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.8.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.708', 'subgroup_hash': 708, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:C_{24}', 'supersolvable': False, 'sylow': 0}
    • id: 223365178
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.710', 'subgroup_hash': 710, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365189
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.8368', 'subgroup_hash': 8368, 'subgroup_order': 576, 'subgroup_tex': 'D_4\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365200
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.9.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.5163', 'subgroup_hash': 5163, 'subgroup_order': 576, 'subgroup_tex': 'C_8\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
    • id: 223365211
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.751', 'subgroup_hash': 751, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365222
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.751', 'subgroup_hash': 751, 'subgroup_order': 432, 'subgroup_tex': 'C_6\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365234
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.752', 'subgroup_hash': 752, 'subgroup_order': 432, 'subgroup_tex': 'C_6:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365245
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.752', 'subgroup_hash': 752, 'subgroup_order': 432, 'subgroup_tex': 'C_6:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365256
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.736', 'subgroup_hash': 736, 'subgroup_order': 432, 'subgroup_tex': 'S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365267
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.736', 'subgroup_hash': 736, 'subgroup_order': 432, 'subgroup_tex': 'S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365278
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.736', 'subgroup_hash': 736, 'subgroup_order': 432, 'subgroup_tex': 'S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365289
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.736', 'subgroup_hash': 736, 'subgroup_order': 432, 'subgroup_tex': 'S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365292
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
    • id: 223365293
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.753', 'subgroup_hash': 753, 'subgroup_order': 432, 'subgroup_tex': 'C_3^2:C_4\\times D_6', 'supersolvable': False, 'sylow': 0}
    • id: 223365294
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 72, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.741', 'subgroup_hash': 741, 'subgroup_order': 432, 'subgroup_tex': 'S_3^3:C_2', 'supersolvable': False, 'sylow': 0}
    • id: 223365295
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.736', 'subgroup_hash': 736, 'subgroup_order': 432, 'subgroup_tex': 'S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365297
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.736', 'subgroup_hash': 736, 'subgroup_order': 432, 'subgroup_tex': 'S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365298
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.736', 'subgroup_hash': 736, 'subgroup_order': 432, 'subgroup_tex': 'S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365299
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '432.736', 'subgroup_hash': 736, 'subgroup_order': 432, 'subgroup_tex': 'S_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365300
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 324, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365301
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 324, 'counter': 64, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.16.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365302
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 324, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365303
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 324, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 223365304
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 324, 'counter': 67, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365305
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 68, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365306
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 324, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.170', 'subgroup_hash': 170, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365308
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 324, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.161', 'subgroup_hash': 161, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 223365309
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 324, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.tb.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.163', 'subgroup_hash': 163, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365310
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365311
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.16.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365312
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365313
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.16.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.168', 'subgroup_hash': 168, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365314
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365315
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.162', 'subgroup_hash': 162, 'subgroup_order': 324, 'subgroup_tex': 'C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365316
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365317
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1030', 'subgroup_hash': 1030, 'subgroup_order': 288, 'subgroup_tex': 'C_2^2\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365319
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.1030', 'subgroup_hash': 1030, 'subgroup_order': 288, 'subgroup_tex': 'C_2^2\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365320
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.867', 'subgroup_hash': 867, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_8', 'supersolvable': False, 'sylow': 0}
    • id: 223365321
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.867', 'subgroup_hash': 867, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:C_8', 'supersolvable': False, 'sylow': 0}
    • id: 223365322
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.936', 'subgroup_hash': 936, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times D_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365323
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.437', 'subgroup_hash': 437, 'subgroup_order': 288, 'subgroup_tex': 'C_8\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365324
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.437', 'subgroup_hash': 437, 'subgroup_order': 288, 'subgroup_tex': 'C_8\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 223365325
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.374', 'subgroup_hash': 374, 'subgroup_order': 288, 'subgroup_tex': 'S_3^2:C_8', 'supersolvable': False, 'sylow': 0}
    • id: 223365326
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.374', 'subgroup_hash': 374, 'subgroup_order': 288, 'subgroup_tex': 'S_3^2:C_8', 'supersolvable': False, 'sylow': 0}
    • id: 223365327
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.877', 'subgroup_hash': 877, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times \\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
    • id: 223365328
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.414', 'subgroup_hash': 414, 'subgroup_order': 288, 'subgroup_tex': 'C_3^2:C_4\\times C_8', 'supersolvable': False, 'sylow': 0}
    • id: 223365330
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.380', 'subgroup_hash': 380, 'subgroup_order': 288, 'subgroup_tex': 'C_4.\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
    • id: 223365331
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.863', 'subgroup_hash': 863, 'subgroup_order': 288, 'subgroup_tex': 'C_4\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365332
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.864', 'subgroup_hash': 864, 'subgroup_order': 288, 'subgroup_tex': 'C_4:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 223365333
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 223365334
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.168', 'subgroup_hash': 168, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 223365335
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365336
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.169', 'subgroup_hash': 169, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 223365337
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
    • id: 223365338
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
    • id: 223365339
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
    • id: 223364791
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '5184.tb', 'ambient_counter': 496, 'ambient_order': 5184, 'ambient_tex': 'F_9\\times \\SOPlus(4,2)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5184.tb.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.156', 'subgroup_hash': 156, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:C_4\\times S_3', 'supersolvable': False, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 551 matching records in this table.
    • id: 223364789
      {'ambient': '5184.tb', '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': '5184.a1.a1', 'complements': ['5184.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '9.a1.a1', '9.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1899, 3122, 1048, 7539, 7534, 3108, 8596, 7659], 'generators': [1, 4032, 2592, 4, 1728, 24, 2, 192, 400, 144], 'label': '5184.tb.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364790
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'contains': ['8.a1.b1', '8.d1.a1', '8.f1.b1', '8.k1.b1', '8.l1.b1', '12.e1.b1', '36.h1.b1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [3322, 3687, 2947, 6894, 6491, 4453, 7066, 7109], 'generators': [1320, 16, 192, 2, 4, 1728, 2304, 2592], 'label': '5184.tb.4.a1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.b1', '2.c1.a1'], 'normal_contains': ['8.a1.b1', '8.d1.a1', '8.f1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364791
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '12.e1.b1'], 'contains': ['48.d1.b1', '48.m1.b1', '48.o1.b1', '72.d1.b1', '216.f1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3762, -1, 3067, -1, 5345, -1, 6160, -1], 'generators': [1320, 2304, 192, 2594, 4, 16], 'label': '5184.tb.24.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.d1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364792
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.e1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.d1.a1', '48.f1.a1', '48.h1.a1', '48.k1.a1', '48.p1.b1', '72.e1.a1', '72.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5641, -1, 7872, -1, 2209, -1, 1491, -1], 'generators': [24, 4032, 192, 2592, 4, 400], 'label': '5184.tb.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364793
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.e1.b1'], 'contains': ['48.a1.b1', '48.b1.b1', '48.d1.b1', '48.f1.b1', '48.h1.b1', '48.k1.b1', '48.p1.a1', '72.e1.b1', '72.i1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5641, -1, 4800, -1, 2209, -1, 4173, -1], 'generators': [1320, 2304, 192, 2592, 4, 400], 'label': '5184.tb.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.e1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364794
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.f1.a1'], 'contains': ['48.c1.a1', '48.g1.a1', '48.i1.a1', '48.j1.a1', '48.q1.b1', '72.i1.a1', '72.k1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8067, -1, 8903, -1, 3234, -1, 1410, -1], 'generators': [24, 1728, 4032, 2592, 4, 400], 'label': '5184.tb.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '24.f1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 223364795
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.f1.a1'], 'contains': ['48.c1.b1', '48.g1.b1', '48.i1.b1', '48.j1.a1', '48.q1.a1', '72.i1.b1', '72.k1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [8067, -1, 5114, -1, 3234, -1, 4256, -1], 'generators': [1320, 1728, 2304, 2592, 4, 400], 'label': '5184.tb.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '24.f1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 223364796
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.f1.a1'], 'contains': ['48.i1.a1', '48.q1.a1', '48.s1.a1', '72.l1.a1', '216.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9499, -1, 7065, -1, 3750, -1, 2928, -1], 'generators': [24, 1728, 4032, 148, 2592, 400], 'label': '5184.tb.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '24.g1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 223364797
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.f1.a1'], 'contains': ['48.i1.b1', '48.q1.b1', '48.s1.a1', '72.l1.b1', '216.d1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [9499, -1, 7120, -1, 3750, -1, 2645, -1], 'generators': [28, 1728, 4032, 148, 2592, 400], 'label': '5184.tb.24.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '24.g1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.b1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 223364798
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.f1.a1'], 'contains': ['48.i1.a1', '48.i1.b1', '48.r1.a1', '72.a1.a1', '216.h1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9960, -1, 7578, -1, 4368, -1, 2467, -1], 'generators': [24, 1728, 4032, 144, 400, 2592], 'label': '5184.tb.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.h1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 223364799
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.f1.a1'], 'contains': ['48.j1.a1', '48.r1.a1', '48.s1.a1', '72.n1.a1', '216.o1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9370, -1, 7214, -1, 3978, -1, 2761, -1], 'generators': [144, 1728, 576, 4, 288, 400], 'label': '5184.tb.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '24.i1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 223364800
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.e1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.k1.a1', '48.l1.a1', '48.o1.a1', '72.u1.a1', '216.i1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3143, -1, 3238, -1, 6740, -1, 6821, -1], 'generators': [2, 4032, 192, 2592, 4, 16], 'label': '5184.tb.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.j1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364801
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.a1.a1', '8.f1.b1', '8.g1.a1', '36.d1.a1', '36.i1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4630, 5690, 4108, 4545, 4116, 5536, 4607, 4770], 'generators': [24, 16, 192, 146, 4, 1728, 4032, 2592], 'label': '5184.tb.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.f1.b1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364802
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.e1.b1', '12.g1.b1', '12.h1.b1'], 'contains': ['48.k1.b1', '48.l1.b1', '48.o1.b1', '72.u1.a1', '216.i1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3143, -1, 2267, -1, 6740, -1, 7159, -1], 'generators': [2, 2304, 192, 2592, 4, 16], 'label': '5184.tb.24.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.j1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364803
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.e1.a1'], 'contains': ['48.k1.a1', '48.m1.a1', '48.n1.a1', '72.w1.a1', '216.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4355, -1, 4452, -1, 4711, -1, 4946, -1], 'generators': [26, 4032, 192, 2592, 4, 16], 'label': '5184.tb.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.k1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364804
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.b1', '12.e1.b1'], 'contains': ['48.k1.b1', '48.m1.b1', '48.n1.b1', '72.w1.b1', '216.j1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4355, -1, 3545, -1, 4711, -1, 5867, -1], 'generators': [1326, 2304, 192, 2592, 4, 400], 'label': '5184.tb.24.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.k1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364805
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.a1.a1', '12.c1.a1', '12.g1.a1'], 'contains': ['48.l1.a1', '72.b1.a1', '216.k1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1593, -1, 1244, -1, 8000, -1, 8527, -1], 'generators': [1, 192, 400, 4032, 2, 4], 'label': '5184.tb.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.l1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364806
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.a1.b1', '12.c1.b1', '12.g1.b1'], 'contains': ['48.l1.b1', '72.b1.a1', '216.k1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1593, -1, 681, -1, 8000, -1, 8887, -1], 'generators': [1, 192, 400, 2304, 2, 4], 'label': '5184.tb.24.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.l1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.b1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364807
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.a1.a1', '12.d1.a1', '12.h1.a1'], 'contains': ['48.l1.a1', '72.y1.a1', '216.l1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1059, -1, 1925, -1, 8485, -1, 7663, -1], 'generators': [25, 192, 400, 1728, 2, 4], 'label': '5184.tb.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.m1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364808
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '12.a1.b1', '12.d1.b1', '12.h1.b1'], 'contains': ['48.l1.b1', '72.y1.b1', '216.l1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1059, -1, 287, -1, 8485, -1, 9360, -1], 'generators': [1323, 192, 400, 576, 6, 4], 'label': '5184.tb.24.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.m1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.b1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364809
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.b1.a1', '12.c1.a1', '12.h1.a1'], 'contains': ['48.l1.a1', '72.y1.a1', '216.m1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [931, -1, 1812, -1, 8392, -1, 7586, -1], 'generators': [25, 4032, 192, 2, 4, 400], 'label': '5184.tb.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.n1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364810
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '12.b1.b1', '12.c1.b1', '12.h1.b1'], 'contains': ['48.l1.b1', '72.y1.b1', '216.m1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [931, -1, 419, -1, 8392, -1, 9417, -1], 'generators': [1323, 2304, 192, 6, 4, 400], 'label': '5184.tb.24.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '24.n1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364811
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.b1.a1', '12.d1.a1', '12.g1.a1'], 'contains': ['48.l1.a1', '72.z1.a1', '216.n1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2861, -1, 1394, -1, 8206, -1, 8470, -1], 'generators': [2593, 4032, 192, 2, 4, 400], 'label': '5184.tb.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364812
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.a1.b1', '8.f1.a1', '8.g1.a1', '36.d1.b1', '36.i1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4630, 5690, 4524, 3256, 4116, 5536, 4838, 3486], 'generators': [26, 16, 192, 146, 4, 1728, 4032, 2592], 'label': '5184.tb.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.a1.b1', '8.f1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364813
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.b1.b1', '12.d1.b1', '12.g1.b1'], 'contains': ['48.l1.b1', '72.z1.a1', '216.n1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2861, -1, 737, -1, 8206, -1, 8811, -1], 'generators': [2593, 2304, 192, 2, 4, 400], 'label': '5184.tb.24.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '24.o1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364814
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.f1.a1'], 'contains': ['48.q1.a1', '48.q1.b1', '48.r1.a1', '72.bc1.a1', '216.p1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9781, -1, 7690, -1, 4198, -1, 2571, -1], 'generators': [28, 1728, 4032, 144, 2592, 400], 'label': '5184.tb.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '24.p1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 223364815
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.c1.a1', '16.d1.a1', '16.h1.a1', '16.h1.b1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.a1.a1', '96.e1.a1', '96.f1.a1', '96.f1.b1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4771, 3366, 5547, 6458, 3973, 3330, 4809, 6629], 'generators': [4, 192, 4032, 1728, 400], 'label': '5184.tb.32.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.b1.a1', '16.c1.a1', '16.d1.a1'], 'normal_contains': ['64.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '576.8368'}
    • id: 223364816
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.a1.b1', '16.b1.a1', '16.e1.a1', '16.e1.b1', '16.f1.a1', '16.g1.a1'], 'contains': ['64.a1.a1', '96.g1.a1', '96.g1.b1', '96.h1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7437, 6769, 8226, 3060, 1740, 6291, 1841, 3311], 'generators': [2592, 1728, 400, 192, 4032], 'label': '5184.tb.32.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1', '16.a1.b1', '16.b1.a1', '16.e1.a1', '16.e1.b1', '16.f1.a1', '16.g1.a1'], 'normal_contains': ['64.a1.a1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '576.5163'}
    • id: 223364817
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.i1.a1', '16.i1.b1', '16.k1.a1'], 'contains': ['64.a1.a1', '96.m1.a1', '96.m1.b1', '96.n1.a1', '96.n1.b1', '96.o1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6730, 4572, 6844, 5350, 575, 4453, 1735, 5570], 'generators': [2596, 1728, 400, 192, 4032], 'label': '5184.tb.32.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.b1.a1'], 'normal_contains': ['64.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364818
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.h1.a1', '16.i1.a1'], 'contains': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1', '96.d1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7085, -1, 8508, -1, 1014, -1, 834, -1], 'generators': [24, 4032, 400, 192, 1728], 'label': '5184.tb.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.d1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.106'}
    • id: 223364819
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '192.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.b1', '16.h1.b1', '16.i1.b1'], 'contains': ['64.a1.a1', '96.a1.b1', '96.b1.b1', '96.c1.b1', '96.d1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7085, -1, 6017, -1, 1014, -1, 3206, -1], 'generators': [1320, 2304, 400, 192, 1728], 'label': '5184.tb.32.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '32.d1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': '96.106'}
    • id: 223364820
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '16.h1.b1', '16.i1.b1'], 'contains': ['64.a1.a1', '96.i1.a1', '96.j1.a1', '96.k1.a1', '96.l1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6907, -1, 5275, -1, 872, -1, 4084, -1], 'generators': [1324, 2304, 1728, 400, 192], 'label': '5184.tb.32.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '32.e1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.a1', 'subgroup_fusion': None, 'weyl_group': '864.4681'}
    • id: 223364821
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '16.h1.a1', '16.i1.a1'], 'contains': ['64.a1.a1', '96.i1.b1', '96.j1.b1', '96.k1.b1', '96.l1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6907, -1, 8735, -1, 872, -1, 652, -1], 'generators': [28, 4032, 1728, 400, 192], 'label': '5184.tb.32.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '32.e1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.e1.b1', 'subgroup_fusion': None, 'weyl_group': '864.4681'}
    • id: 223364822
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.c1.a1', '18.a1.a1'], 'contains': ['72.b1.a1', '72.c1.a1', '72.y1.a1', '324.a1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1047, -1, 936, -1, 8112, -1, 8374, -1], 'generators': [1, 192, 400, 24, 2, 4], 'label': '5184.tb.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
    • id: 223364823
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.e1.a1', '8.j1.a1', '12.f1.a1', '36.g1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6519, 7823, 6885, 2282, 3229, 7612, 2377, 2514], 'generators': [24, 400, 192, 144, 2592, 1728, 4032, 4], 'label': '5184.tb.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.e1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364824
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.c1.b1', '18.a1.b1'], 'contains': ['72.b1.a1', '72.c1.b1', '72.y1.b1', '324.a1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1047, -1, 429, -1, 8112, -1, 9292, -1], 'generators': [1, 192, 400, 1320, 2, 4], 'label': '5184.tb.36.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '36.a1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.b1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
    • id: 223364825
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.d1.a1', '18.a1.a1'], 'contains': ['72.c1.a1', '72.y1.a1', '72.z1.a1', '324.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1515, -1, 1059, -1, 8299, -1, 7887, -1], 'generators': [2593, 192, 400, 24, 2, 4], 'label': '5184.tb.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
    • id: 223364826
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.d1.b1', '18.a1.b1'], 'contains': ['72.c1.b1', '72.y1.b1', '72.z1.a1', '324.b1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1515, -1, 600, -1, 8299, -1, 9224, -1], 'generators': [3745, 192, 400, 1320, 2, 4], 'label': '5184.tb.36.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '36.b1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.b1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
    • id: 223364827
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '72.e1.a1', '72.u1.a1', '72.w1.a1', '324.c1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2520, -1, 2367, -1, 6212, -1, 6400, -1], 'generators': [24, 192, 16, 2, 2592, 4], 'label': '5184.tb.36.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364828
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '18.a1.b1', '18.b1.b1', '18.c1.a1'], 'contains': ['72.c1.b1', '72.d1.b1', '72.e1.b1', '72.u1.a1', '72.w1.b1', '324.c1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2520, -1, 2589, -1, 6212, -1, 6925, -1], 'generators': [4200, 192, 16, 2, 2592, 4], 'label': '5184.tb.36.c1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.c1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364829
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '18.c1.a1'], 'contains': ['72.e1.a1', '72.w1.b1', '72.x1.a1', '324.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4358, -1, 3866, -1, 3847, -1, 4569, -1], 'generators': [24, 192, 16, 4178, 2592, 4], 'label': '5184.tb.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1030'}
    • id: 223364830
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '18.c1.a1'], 'contains': ['72.e1.b1', '72.w1.a1', '72.x1.a1', '324.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4358, -1, 3750, -1, 3847, -1, 4809, -1], 'generators': [26, 192, 16, 4178, 2592, 4], 'label': '5184.tb.36.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': '288.1030'}
    • id: 223364831
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '18.d1.a1'], 'contains': ['72.g1.a1', '72.q1.a1', '72.r1.a1', '108.a1.a1', '108.c1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1173, -1, 1593, -1, 9244, -1, 8279, -1], 'generators': [1, 4032, 4, 24, 1728, 2], 'label': '5184.tb.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.e1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 223364832
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '18.d1.b1'], 'contains': ['72.g1.b1', '72.q1.a1', '72.r1.b1', '108.a1.b1', '108.c1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1173, -1, 141, -1, 9244, -1, 9964, -1], 'generators': [1, 2304, 4, 4200, 1728, 2], 'label': '5184.tb.36.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '36.e1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 223364833
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '18.d1.a1'], 'contains': ['72.g1.a1', '72.r1.a1', '72.s1.a1', '108.b1.a1', '108.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1677, -1, 1731, -1, 9647, -1, 8091, -1], 'generators': [2593, 1728, 4032, 24, 2, 4], 'label': '5184.tb.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.f1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 223364834
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.g1.a1', '36.k1.a1', '36.p1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3481, 4764, 3862, 5212, 6261, 3403, 5300, 5433], 'generators': [144, 16, 192, 2, 4, 1728, 576, 288], 'label': '5184.tb.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.d1.a1', '8.e1.a1', '8.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364835
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '18.d1.b1'], 'contains': ['72.g1.b1', '72.r1.b1', '72.s1.a1', '108.b1.b1', '108.d1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1677, -1, 222, -1, 9647, -1, 9628, -1], 'generators': [2593, 1728, 4032, 4200, 2, 4], 'label': '5184.tb.36.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.b1', 'old_label': '36.f1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 223364836
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '18.c1.a1'], 'contains': ['72.e1.a1', '72.e1.b1', '72.f1.a1', '72.f1.b1', '72.j1.a1', '72.v1.a1', '72.bb1.a1', '108.f1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6593, -1, 6671, -1, 3379, -1, 2349, -1], 'generators': [24, 192, 400, 4176, 4, 2592], 'label': '5184.tb.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1030'}
    • id: 223364837
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '18.d1.a1', '18.e1.a1', '18.f1.a1'], 'contains': ['72.g1.a1', '72.h1.a1', '72.k1.a1', '72.m1.a1', '72.o1.a1', '108.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3257, -1, 4105, -1, 7355, -1, 6712, -1], 'generators': [24, 1728, 4032, 2, 2592, 4], 'label': '5184.tb.36.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.h1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364838
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '18.d1.b1', '18.e1.b1', '18.f1.a1'], 'contains': ['72.g1.b1', '72.h1.b1', '72.k1.b1', '72.m1.a1', '72.o1.b1', '108.e1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [3257, -1, 2497, -1, 7355, -1, 7248, -1], 'generators': [1320, 1728, 2304, 2, 2592, 4], 'label': '5184.tb.36.h1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.h1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364839
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '18.f1.a1'], 'contains': ['72.k1.a1', '72.o1.b1', '72.p1.a1', '324.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5176, -1, 3560, -1, 5029, -1, 4629, -1], 'generators': [24, 1728, 4032, 146, 2592, 4], 'label': '5184.tb.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.i1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364840
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '18.f1.a1'], 'contains': ['72.k1.b1', '72.o1.a1', '72.p1.a1', '324.d1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5176, -1, 4606, -1, 5029, -1, 4868, -1], 'generators': [26, 1728, 4032, 146, 2592, 4], 'label': '5184.tb.36.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.i1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364841
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.f1.a1'], 'contains': ['72.a1.a1', '72.k1.a1', '72.k1.b1', '72.l1.a1', '72.l1.b1', '72.n1.a1', '72.bc1.a1', '324.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8180, -1, 7337, -1, 5169, -1, 3830, -1], 'generators': [24, 1728, 4032, 144, 4, 2592], 'label': '5184.tb.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.j1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364842
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '18.f1.a1', '18.g1.a1', '18.h1.a1'], 'contains': ['72.m1.a1', '72.n1.a1', '72.p1.a1', '324.f1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3439, -1, 4192, -1, 7177, -1, 5403, -1], 'generators': [144, 1728, 576, 2, 288, 4], 'label': '5184.tb.36.k1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.k1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364843
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '18.d1.a1', '18.d1.b1', '18.g1.a1'], 'contains': ['72.m1.a1', '72.q1.a1', '72.s1.a1', '108.g1.a1', '108.g1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2060, -1, 1191, -1, 9045, -1, 8964, -1], 'generators': [1, 1728, 4032, 2592, 2, 4], 'label': '5184.tb.36.l1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.l1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364844
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '18.d1.a1', '18.e1.b1', '18.h1.a1'], 'contains': ['72.m1.a1', '72.r1.a1', '108.h1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [606, -1, 1928, -1, 9851, -1, 7966, -1], 'generators': [25, 1728, 4032, 2592, 2, 4], 'label': '5184.tb.36.m1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.m1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364845
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.d1.a1'], 'contains': ['8.d1.a1', '8.h1.a1', '8.i1.a1', '12.g1.a1', '12.g1.b1', '36.l1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3079, 908, 1250, 9489, 7794, 879, 8500, 9694], 'generators': [1, 400, 192, 2592, 4, 1728, 4032, 2], 'label': '5184.tb.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.a1.a1', '2.a1.b1', '2.d1.a1'], 'normal_contains': ['8.d1.a1', '8.h1.a1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364846
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '18.d1.b1', '18.e1.a1', '18.h1.a1'], 'contains': ['72.m1.a1', '72.r1.b1', '108.h1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [606, -1, 40, -1, 9851, -1, 9772, -1], 'generators': [1321, 1728, 2304, 2592, 2, 4], 'label': '5184.tb.36.m1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.m1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.b1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364847
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '18.e1.a1', '18.e1.b1', '18.g1.a1'], 'contains': ['72.m1.a1', '72.t1.a1', '324.i1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [384, -1, 2039, -1, 8623, -1, 8738, -1], 'generators': [145, 1728, 4032, 2592, 290, 4], 'label': '5184.tb.36.n1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.n1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364848
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '18.f1.a1'], 'contains': ['72.n1.a1', '72.o1.a1', '72.o1.b1', '324.j1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5334, -1, 2896, -1, 5851, -1, 5518, -1], 'generators': [26, 1728, 4032, 144, 2592, 4], 'label': '5184.tb.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.o1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 223364849
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '18.c1.a1', '18.i1.a1', '18.j1.a1'], 'contains': ['72.u1.a1', '72.v1.a1', '72.x1.a1', '324.f1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2280, -1, 3121, -1, 6040, -1, 5180, -1], 'generators': [144, 192, 16, 2, 288, 4], 'label': '5184.tb.36.p1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364850
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '648.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.g1.b1', '18.a1.a1', '18.a1.b1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.u1.a1', '72.z1.a1', '324.g1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1869, -1, 830, -1, 7650, -1, 8634, -1], 'generators': [1, 192, 400, 2592, 2, 4], 'label': '5184.tb.36.q1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.q1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
    • id: 223364851
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.a1.a1', '18.b1.b1', '18.j1.a1'], 'contains': ['72.u1.a1', '72.y1.a1', '324.h1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [771, -1, 1265, -1, 7825, -1, 7751, -1], 'generators': [25, 192, 400, 2592, 2, 4], 'label': '5184.tb.36.r1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.r1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.a1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364852
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '18.a1.b1', '18.b1.a1', '18.j1.a1'], 'contains': ['72.u1.a1', '72.y1.b1', '324.h1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [771, -1, 533, -1, 7825, -1, 9136, -1], 'generators': [4203, 192, 400, 2592, 6, 4], 'label': '5184.tb.36.r1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.r1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.b1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364853
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '18.b1.a1', '18.b1.b1', '18.i1.a1'], 'contains': ['72.u1.a1', '72.ba1.a1', '324.i1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [210, -1, 1426, -1, 7539, -1, 7819, -1], 'generators': [145, 192, 400, 288, 290, 4], 'label': '5184.tb.36.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.s1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.a1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364854
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '18.c1.a1'], 'contains': ['72.v1.a1', '72.w1.a1', '72.w1.b1', '324.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4559, -1, 3483, -1, 4546, -1, 5301, -1], 'generators': [26, 192, 16, 4176, 2592, 4], 'label': '5184.tb.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.t1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': '288.1030'}
    • id: 223364855
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.a1.a1', '24.b1.a1', '24.e1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '96.j1.b1', '144.d1.a1', '144.e1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4879, -1, 7797, -1, 2209, -1, 1307, -1], 'generators': [24, 192, 4, 1728, 400], 'label': '5184.tb.48.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364856
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'contains': ['8.d1.a1', '8.m1.a1', '12.h1.a1', '36.m1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [995, 2639, 1968, 8246, 8428, 2564, 7739, 9052], 'generators': [25, 400, 192, 2592, 4, 1728, 4032, 2], 'label': '5184.tb.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.e1.a1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364857
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '24.a1.b1', '24.b1.b1', '24.e1.b1'], 'contains': ['96.a1.b1', '96.f1.b1', '96.j1.a1', '144.d1.b1', '144.e1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4879, -1, 4639, -1, 2209, -1, 4982, -1], 'generators': [1320, 192, 4, 576, 400], 'label': '5184.tb.48.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '48.a1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.b1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364858
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.e1.a1'], 'contains': ['96.a1.a1', '96.l1.b1', '96.n1.a1', '144.f1.a1', '144.g1.a1', '144.h1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6096, -1, 8147, -1, 717, -1, 747, -1], 'generators': [24, 1728, 2596, 400, 192], 'label': '5184.tb.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364859
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '24.e1.b1'], 'contains': ['96.a1.b1', '96.l1.a1', '96.n1.b1', '144.f1.b1', '144.g1.b1', '144.h1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6096, -1, 5444, -1, 717, -1, 3722, -1], 'generators': [4200, 576, 2596, 400, 192], 'label': '5184.tb.48.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '48.b1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364860
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.f1.a1'], 'contains': ['96.d1.a1', '96.e1.a1', '96.k1.b1', '144.d1.a1', '144.j1.a1', '144.k1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7567, -1, 8968, -1, 2471, -1, 912, -1], 'generators': [24, 4032, 4, 1728, 400], 'label': '5184.tb.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.a1', 'old_label': '48.c1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 223364861
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1728.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '24.f1.b1'], 'contains': ['96.d1.b1', '96.e1.a1', '96.k1.a1', '144.d1.b1', '144.j1.b1', '144.k1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [7567, -1, 4860, -1, 2471, -1, 4684, -1], 'generators': [4200, 2304, 4, 1728, 400], 'label': '5184.tb.48.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.b1', 'old_label': '48.c1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
    • id: 223364862
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1'], 'contains': ['96.c1.a1', '96.f1.a1', '96.l1.b1', '144.e1.a1', '144.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4738, -1, 7879, -1, 2071, -1, 1391, -1], 'generators': [24, 4032, 4, 400, 192], 'label': '5184.tb.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364863
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.b1', '24.c1.b1', '24.d1.b1', '24.e1.b1'], 'contains': ['96.c1.b1', '96.f1.b1', '96.l1.a1', '144.e1.b1', '144.k1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4738, -1, 4721, -1, 2071, -1, 4898, -1], 'generators': [1320, 2304, 4, 400, 192], 'label': '5184.tb.48.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '48.d1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364864
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1'], 'contains': ['96.b1.a1', '96.i1.b1', '96.m1.a1', '144.g1.a1', '144.l1.a1', '144.m1.a1'], 'core': '5184.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7853, -1, 9260, -1, 412, -1, 244, -1], 'generators': [24, 4032, 2596, 400, 3648], 'label': '5184.tb.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.e1.a1', 'old_label': '48.e1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 223364865
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1'], 'contains': ['96.b1.b1', '96.i1.a1', '96.m1.b1', '144.g1.b1', '144.l1.b1', '144.m1.b1'], 'core': '5184.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [7853, -1, 5899, -1, 412, -1, 3632, -1], 'generators': [1320, 2304, 2596, 400, 3648], 'label': '5184.tb.48.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.e1.b1', 'old_label': '48.e1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 223364866
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.e1.a1'], 'contains': ['96.c1.a1', '96.j1.b1', '96.n1.a1', '144.h1.a1', '144.l1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5886, -1, 8058, -1, 1147, -1, 1072, -1], 'generators': [24, 4032, 2596, 400, 192], 'label': '5184.tb.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.f1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364867
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.a1', '2.e1.a1'], 'contains': ['8.d1.a1', '8.m1.b1', '12.h1.b1', '36.m1.b1'], 'core': '4.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [995, 2639, 502, 8845, 8428, 2564, 9184, 8456], 'generators': [1323, 400, 192, 2592, 4, 1728, 2304, 6], 'label': '5184.tb.4.f1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.a1', '2.e1.a1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364868
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '24.e1.b1'], 'contains': ['96.c1.b1', '96.j1.a1', '96.n1.b1', '144.h1.b1', '144.l1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5886, -1, 4977, -1, 1147, -1, 3366, -1], 'generators': [1320, 2304, 2596, 400, 192], 'label': '5184.tb.48.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '48.f1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364869
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.f1.a1'], 'contains': ['96.d1.a1', '96.k1.b1', '96.o1.a1', '144.f1.a1', '144.l1.a1', '144.m1.a1', '144.n1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8489, -1, 9056, -1, 1284, -1, 562, -1], 'generators': [24, 1728, 2596, 400, 4032], 'label': '5184.tb.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.a1', 'old_label': '48.g1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 223364870
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.b1', '24.f1.b1'], 'contains': ['96.d1.b1', '96.k1.a1', '96.o1.a1', '144.f1.b1', '144.l1.b1', '144.m1.b1', '144.n1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8489, -1, 5664, -1, 1284, -1, 4256, -1], 'generators': [4200, 1728, 2596, 400, 2304], 'label': '5184.tb.48.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.b1', 'old_label': '48.g1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.b1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
    • id: 223364871
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.e1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.g1.a1', '144.i1.a1', '144.o1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6314, -1, 8247, -1, 1575, -1, 1486, -1], 'generators': [24, 4032, 2592, 400, 192], 'label': '5184.tb.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.h1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '48.4'}
    • id: 223364872
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.b1', '24.e1.b1'], 'contains': ['96.a1.b1', '96.c1.b1', '96.g1.b1', '144.i1.b1', '144.o1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6314, -1, 6027, -1, 1575, -1, 3114, -1], 'generators': [1320, 2304, 2592, 400, 192], 'label': '5184.tb.48.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '48.h1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.b1', 'subgroup_fusion': None, 'weyl_group': '48.4'}
    • id: 223364873
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1'], 'contains': ['96.d1.a1', '96.h1.a1', '144.a1.a1', '144.o1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [9119, -1, 8840, -1, 3234, -1, 1578, -1], 'generators': [24, 1728, 2592, 400, 4032], 'label': '5184.tb.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '48.i1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 223364874
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '576.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.b1', '24.f1.b1', '24.g1.b1', '24.h1.a1'], 'contains': ['96.d1.b1', '96.h1.a1', '144.a1.b1', '144.o1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9119, -1, 6489, -1, 3234, -1, 3285, -1], 'generators': [1320, 1728, 2592, 400, 2304], 'label': '5184.tb.48.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '48.i1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': '144.186'}
    • id: 223364875
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.f1.a1', '24.f1.b1', '24.i1.a1'], 'contains': ['96.e1.a1', '96.h1.a1', '96.o1.a1', '144.p1.a1', '144.t1.a1', '144.t1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8678, -1, 7190, -1, 3367, -1, 2942, -1], 'generators': [2592, 1728, 4, 400, 4032], 'label': '5184.tb.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '48.j1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '432.741'}
    • id: 223364876
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.e1.a1', '24.j1.a1', '24.k1.a1'], 'contains': ['96.f1.a1', '96.g1.a1', '96.n1.a1', '144.t1.a1', '144.u1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5084, -1, 6892, -1, 2729, -1, 2590, -1], 'generators': [2592, 4032, 4, 400, 192], 'label': '5184.tb.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.k1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364877
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.e1.b1', '24.j1.b1', '24.k1.b1'], 'contains': ['96.f1.b1', '96.g1.b1', '96.n1.b1', '144.t1.b1', '144.u1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5084, -1, 4558, -1, 2729, -1, 3549, -1], 'generators': [2592, 2304, 4, 400, 192], 'label': '5184.tb.48.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '48.k1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364878
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5184.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.b1.b1', '2.d1.a1'], 'contains': ['8.d1.a1', '8.n1.a1', '36.n1.a1', '36.s1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [324, 1806, 2095, 7647, 7226, 1753, 7831, 7859], 'generators': [145, 400, 192, 2592, 4, 1728, 4032, 290], 'label': '5184.tb.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.b1.a1', '2.b1.b1', '2.d1.a1'], 'normal_contains': ['8.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '5184.tb'}
    • id: 223364879
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.c1.a1', '24.j1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1'], 'contains': ['96.f1.a1', '144.b1.a1', '432.k1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2803, -1, 3140, -1, 7157, -1, 7066, -1], 'generators': [2, 192, 4032, 4, 16], 'label': '5184.tb.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.l1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364880
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '288.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.b1', '24.c1.b1', '24.j1.b1', '24.l1.b1', '24.m1.b1', '24.n1.b1', '24.o1.b1'], 'contains': ['96.f1.b1', '144.b1.a1', '432.k1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2803, -1, 2069, -1, 7157, -1, 7507, -1], 'generators': [2, 192, 2304, 4, 16], 'label': '5184.tb.48.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '48.l1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.b1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364881
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.a1.a1', '24.d1.a1', '24.k1.a1'], 'contains': ['96.f1.a1', '144.v1.a1', '432.l1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4196, -1, 4298, -1, 5114, -1, 5388, -1], 'generators': [26, 192, 1728, 4, 16], 'label': '5184.tb.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.m1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364882
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '24.a1.b1', '24.d1.b1', '24.k1.b1'], 'contains': ['96.f1.b1', '144.v1.b1', '432.l1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4196, -1, 3539, -1, 5114, -1, 6185, -1], 'generators': [1326, 192, 576, 4, 400], 'label': '5184.tb.48.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '48.m1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.b1', 'subgroup_fusion': None, 'weyl_group': '144.185'}
    • id: 223364883
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.b1.a1', '24.c1.a1', '24.k1.a1'], 'contains': ['96.f1.a1', '144.v1.a1', '432.m1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4047, -1, 4193, -1, 5259, -1, 5280, -1], 'generators': [26, 4032, 4, 16, 192], 'label': '5184.tb.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.n1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364884
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '864.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '24.b1.b1', '24.c1.b1', '24.k1.b1'], 'contains': ['96.f1.b1', '144.v1.b1', '432.m1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4047, -1, 3452, -1, 5259, -1, 6274, -1], 'generators': [1326, 2304, 4, 400, 192], 'label': '5184.tb.48.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '48.n1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364885
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.b1.a1', '24.d1.a1', '24.j1.a1'], 'contains': ['96.f1.a1', '144.w1.a1', '432.n1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3725, -1, 3832, -1, 6123, -1, 6021, -1], 'generators': [2594, 4032, 4, 16, 192], 'label': '5184.tb.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.o1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364886
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.b1.b1', '24.d1.b1', '24.j1.b1'], 'contains': ['96.f1.b1', '144.w1.a1', '432.n1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3725, -1, 2940, -1, 6123, -1, 6390, -1], 'generators': [2594, 2304, 4, 16, 192], 'label': '5184.tb.48.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '48.o1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364887
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.e1.b1'], 'contains': ['96.g1.b1', '96.j1.a1', '96.l1.a1', '144.x1.a1', '144.ba1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6572, -1, 5078, -1, 1420, -1, 4173, -1], 'generators': [1324, 2304, 2592, 400, 192], 'label': '5184.tb.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.b1', 'old_label': '48.p1.a1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '432.736'}
    • id: 223364888
      {'ambient': '5184.tb', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2592.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '24.e1.a1'], 'contains': ['96.g1.a1', '96.j1.b1', '96.l1.b1', '144.x1.b1', '144.ba1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6572, -1, 8410, -1, 1420, -1, 1156, -1], 'generators': [28, 4032, 2592, 400, 192], 'label': '5184.tb.48.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.p1.b1', 'projective_image': '5184.tb', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.b1', 'subgroup_fusion': None, 'weyl_group': '432.736'}