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  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [8, 6, 6], 'aut_gens': [[47882431127126422787571329, 9615657570066924399262654138], [1213028380636746709320661037, 5048314978767839256475993724], [1213028380635031132917600053, 6646488899010418747437407585], [469165927488167891950567844, 9180671538730792082423001453]], 'aut_group': None, 'aut_hash': 6899009085423557347, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 629856, 'aut_permdeg': 4536, 'aut_perms': 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729, 2], [9, 648, 2], [12, 1458, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '17496.ec', 'commutator_count': 1, 'commutator_label': '1458.1795', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 107, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 729, 1, 1], [3, 8, 1, 1], [3, 24, 1, 30], [3, 81, 2, 1], [4, 1458, 1, 3], [6, 729, 2, 1], [9, 648, 2, 1], [12, 1458, 2, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 144, 'exponent': 36, 'exponents_of_order': [7, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 27]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '216.160', 'hash': 973806794745079939, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [4, 12], 'inner_gens': [[47882431127126422787571329, 8451722273956368905038817444], [825947257883729079319454158, 9615657570066924399262654138]], 'inner_hash': 973806794745079939, 'inner_nilpotent': False, 'inner_order': 17496, 'inner_split': True, 'inner_tex': 'C_3^2\\wr C_3:Q_8', 'inner_used': [1, 2], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 12], [2, 3], [8, 3], [24, 30]], 'label': '17496.ec', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^2wrC3:Q8', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 48, 'number_divisions': 42, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 566, 'number_subgroup_classes': 9760, 'number_subgroups': 2089932, 'old_label': None, 'order': 17496, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 729], [3, 890], [4, 4374], [6, 1458], [9, 1296], [12, 8748]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6, 6], 'outer_gen_pows': [19289030015041605065368875, 0], 'outer_gens': [[79420772412934806433209653, 8357307336702404813166479057], [33014302651624106797526800, 5081122258363949001897163374]], 'outer_group': '36.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 36, 'outer_permdeg': 8, 'outer_perms': [750, 5761], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times S_3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 1], [8, 1], [16, 1], [24, 30]], 'representations': {'PC': {'code': '358226159667802313593812101054655061982904566909520788564600392486142084152630537065249869570024177105445005320244394531676843961566717514515225919', 'gens': [1, 3, 5, 6, 7, 8, 9, 10], 'pres': [10, -2, -3, -2, -2, -3, 3, 3, 3, 3, 3, 20, 19331, 311582, 90102, 82, 405603, 182653, 794404, 235814, 92224, 234, 357125, 187215, 88105, 755, 346086, 525016, 111746, 2556, 633607, 230417, 143067, 8677, 1172888, 272178, 157348, 29198, 1617609, 613219, 14429, 97239]}, 'Perm': {'d': 27, 'gens': [9615657570066924399262654138, 47882431127126422787571329]}}, 'schur_multiplier': [3, 3], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2\\wr C_3:Q_8', 'transitive_degree': 27, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 153342996
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 107, 'group_order': 17496, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 153343007
      {'aut_label': '2A', 'centralizer': '729.a1', 'counter': 2, 'group_counter': 107, 'group_order': 17496, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 405259588835339686677565492, 'size': 729}
    • id: 153343018
      {'aut_label': '3A', 'centralizer': '8.a1', 'counter': 3, 'group_counter': 107, 'group_order': 17496, 'label': '3A', 'order': 3, 'powers': [3, 1], 'representative': 840788568360280067521688362, 'size': 8}
    • id: 153343029
      {'aut_label': '3B', 'centralizer': '24.a1', 'counter': 4, 'group_counter': 107, 'group_order': 17496, 'label': '3B', 'order': 3, 'powers': [4, 1], 'representative': 77321, 'size': 24}
    • id: 153343039
      {'aut_label': '3C', 'centralizer': '24.a1', 'counter': 5, 'group_counter': 107, 'group_order': 17496, 'label': '3C', 'order': 3, 'powers': [5, 1], 'representative': 504943931194121, 'size': 24}
    • id: 153343040
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 6, 'group_counter': 107, 'group_order': 17496, 'label': '3D', 'order': 3, 'powers': [6, 1], 'representative': 504943931211562, 'size': 24}
    • id: 153343041
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 7, 'group_counter': 107, 'group_order': 17496, 'label': '3E', 'order': 3, 'powers': [7, 1], 'representative': 504943931255490, 'size': 24}
    • id: 153343042
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 8, 'group_counter': 107, 'group_order': 17496, 'label': '3F', 'order': 3, 'powers': [8, 1], 'representative': 504943931291593, 'size': 24}
    • id: 153343043
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 9, 'group_counter': 107, 'group_order': 17496, 'label': '3G', 'order': 3, 'powers': [9, 1], 'representative': 504943931344932, 'size': 24}
    • id: 153342997
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 10, 'group_counter': 107, 'group_order': 17496, 'label': '3H', 'order': 3, 'powers': [10, 1], 'representative': 504943931393280, 'size': 24}
    • id: 153342998
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 11, 'group_counter': 107, 'group_order': 17496, 'label': '3I', 'order': 3, 'powers': [11, 1], 'representative': 504943931424344, 'size': 24}
    • id: 153342999
      {'aut_label': '3B', 'centralizer': '24.a1', 'counter': 12, 'group_counter': 107, 'group_order': 17496, 'label': '3J', 'order': 3, 'powers': [12, 1], 'representative': 504943931441685, 'size': 24}
    • id: 153343000
      {'aut_label': '3B', 'centralizer': '24.a1', 'counter': 13, 'group_counter': 107, 'group_order': 17496, 'label': '3K', 'order': 3, 'powers': [13, 1], 'representative': 513163763437432968023866121, 'size': 24}
    • id: 153343001
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 14, 'group_counter': 107, 'group_order': 17496, 'label': '3L', 'order': 3, 'powers': [14, 1], 'representative': 513163763437432968023883562, 'size': 24}
    • id: 153343002
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 15, 'group_counter': 107, 'group_order': 17496, 'label': '3M', 'order': 3, 'powers': [15, 1], 'representative': 513163763437432968023927490, 'size': 24}
    • id: 153343003
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 16, 'group_counter': 107, 'group_order': 17496, 'label': '3N', 'order': 3, 'powers': [16, 1], 'representative': 513163763437432968023963593, 'size': 24}
    • id: 153343004
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 17, 'group_counter': 107, 'group_order': 17496, 'label': '3O', 'order': 3, 'powers': [17, 1], 'representative': 513163763437432968024016932, 'size': 24}
    • id: 153343005
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 18, 'group_counter': 107, 'group_order': 17496, 'label': '3P', 'order': 3, 'powers': [18, 1], 'representative': 513163763437432968024065280, 'size': 24}
    • id: 153343006
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 19, 'group_counter': 107, 'group_order': 17496, 'label': '3Q', 'order': 3, 'powers': [19, 1], 'representative': 513163763437432968024096344, 'size': 24}
    • id: 153343008
      {'aut_label': '3R', 'centralizer': '24.a1', 'counter': 20, 'group_counter': 107, 'group_order': 17496, 'label': '3R', 'order': 3, 'powers': [20, 1], 'representative': 513163763437688063675328521, 'size': 24}
    • id: 153343009
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 21, 'group_counter': 107, 'group_order': 17496, 'label': '3S', 'order': 3, 'powers': [21, 1], 'representative': 513163763437688063675389890, 'size': 24}
    • id: 153343010
      {'aut_label': '3T', 'centralizer': '24.a1', 'counter': 22, 'group_counter': 107, 'group_order': 17496, 'label': '3T', 'order': 3, 'powers': [22, 1], 'representative': 513163763437688063675425993, 'size': 24}
    • id: 153343011
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 23, 'group_counter': 107, 'group_order': 17496, 'label': '3U', 'order': 3, 'powers': [23, 1], 'representative': 513163763437688063675479332, 'size': 24}
    • id: 153343012
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 24, 'group_counter': 107, 'group_order': 17496, 'label': '3V', 'order': 3, 'powers': [24, 1], 'representative': 513163763437688063675527680, 'size': 24}
    • id: 153343013
      {'aut_label': '3R', 'centralizer': '24.a1', 'counter': 25, 'group_counter': 107, 'group_order': 17496, 'label': '3W', 'order': 3, 'powers': [25, 1], 'representative': 513163763437688063675558744, 'size': 24}
    • id: 153343014
      {'aut_label': '3R', 'centralizer': '24.a1', 'counter': 26, 'group_counter': 107, 'group_order': 17496, 'label': '3X', 'order': 3, 'powers': [26, 1], 'representative': 513163763438062059422746121, 'size': 24}
    • id: 153343015
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 27, 'group_counter': 107, 'group_order': 17496, 'label': '3Y', 'order': 3, 'powers': [27, 1], 'representative': 513163763438062059422843593, 'size': 24}
    • id: 153343016
      {'aut_label': '3R', 'centralizer': '24.a1', 'counter': 28, 'group_counter': 107, 'group_order': 17496, 'label': '3Z', 'order': 3, 'powers': [28, 1], 'representative': 513163763438062059422945280, 'size': 24}
    • id: 153343017
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 29, 'group_counter': 107, 'group_order': 17496, 'label': '3AA', 'order': 3, 'powers': [29, 1], 'representative': 513163763438062059422976344, 'size': 24}
    • id: 153343019
      {'aut_label': '3R', 'centralizer': '24.a1', 'counter': 30, 'group_counter': 107, 'group_order': 17496, 'label': '3AB', 'order': 3, 'powers': [30, 1], 'representative': 513163763438398217480237321, 'size': 24}
    • id: 153343020
      {'aut_label': '3R', 'centralizer': '24.a1', 'counter': 31, 'group_counter': 107, 'group_order': 17496, 'label': '3AC', 'order': 3, 'powers': [31, 1], 'representative': 513163763438398217480388132, 'size': 24}
    • id: 153343021
      {'aut_label': '3D', 'centralizer': '24.a1', 'counter': 32, 'group_counter': 107, 'group_order': 17496, 'label': '3AD', 'order': 3, 'powers': [32, 1], 'representative': 513163763438398217480436480, 'size': 24}
    • id: 153343022
      {'aut_label': '3T', 'centralizer': '24.a1', 'counter': 33, 'group_counter': 107, 'group_order': 17496, 'label': '3AE', 'order': 3, 'powers': [33, 1], 'representative': 513163763438812819706726744, 'size': 24}
    • id: 153343023
      {'aut_label': '3AF1', 'centralizer': '81.a1', 'counter': 34, 'group_counter': 107, 'group_order': 17496, 'label': '3AF1', 'order': 3, 'powers': [35, 1], 'representative': 8390891254698811052360853119, 'size': 81}
    • id: 153343024
      {'aut_label': '3AF1', 'centralizer': '81.a1', 'counter': 35, 'group_counter': 107, 'group_order': 17496, 'label': '3AF-1', 'order': 3, 'powers': [34, 1], 'representative': 6692479687879903049932744664, 'size': 81}
    • id: 153343025
      {'aut_label': '4A', 'centralizer': '1458.a1', 'counter': 36, 'group_counter': 107, 'group_order': 17496, 'label': '4A', 'order': 4, 'powers': [2, 36], 'representative': 1306070915192417555050572777, 'size': 1458}
    • id: 153343026
      {'aut_label': '4A', 'centralizer': '1458.a1', 'counter': 37, 'group_counter': 107, 'group_order': 17496, 'label': '4B', 'order': 4, 'powers': [2, 37], 'representative': 434317255772928734588940169, 'size': 1458}
    • id: 153343027
      {'aut_label': '4A', 'centralizer': '1458.a1', 'counter': 38, 'group_counter': 107, 'group_order': 17496, 'label': '4C', 'order': 4, 'powers': [2, 38], 'representative': 33014302649534101186705146, 'size': 1458}
    • id: 153343028
      {'aut_label': '6A1', 'centralizer': '729.a1', 'counter': 39, 'group_counter': 107, 'group_order': 17496, 'label': '6A1', 'order': 6, 'powers': [34, 2], 'representative': 6291590060604559666374085799, 'size': 729}
    • id: 153343030
      {'aut_label': '6A1', 'centralizer': '729.a1', 'counter': 40, 'group_counter': 107, 'group_order': 17496, 'label': '6A-1', 'order': 6, 'powers': [35, 2], 'representative': 8791624592471040092472443593, 'size': 729}
    • id: 153343031
      {'aut_label': '9A1', 'centralizer': '648.bf1', 'counter': 41, 'group_counter': 107, 'group_order': 17496, 'label': '9A1', 'order': 9, 'powers': [42, 3], 'representative': 10066641403770770606392996634, 'size': 648}
    • id: 153343032
      {'aut_label': '9A1', 'centralizer': '648.bf1', 'counter': 42, 'group_counter': 107, 'group_order': 17496, 'label': '9A-1', 'order': 9, 'powers': [41, 3], 'representative': 6274917809020496866046521410, 'size': 648}
    • id: 153343033
      {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 43, 'group_counter': 107, 'group_order': 17496, 'label': '12A1', 'order': 12, 'powers': [39, 36], 'representative': 7614655330274512916177623265, 'size': 1458}
    • id: 153343034
      {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 44, 'group_counter': 107, 'group_order': 17496, 'label': '12A-1', 'order': 12, 'powers': [40, 36], 'representative': 5388294748717484605033862257, 'size': 1458}
    • id: 153343035
      {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 45, 'group_counter': 107, 'group_order': 17496, 'label': '12B1', 'order': 12, 'powers': [40, 37], 'representative': 6601326447709139935840060595, 'size': 1458}
    • id: 153343036
      {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 46, 'group_counter': 107, 'group_order': 17496, 'label': '12B-1', 'order': 12, 'powers': [39, 37], 'representative': 10839153671918536571445682898, 'size': 1458}
    • id: 153343037
      {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 47, 'group_counter': 107, 'group_order': 17496, 'label': '12C1', 'order': 12, 'powers': [40, 38], 'representative': 5902699403850180024268384100, 'size': 1458}
    • id: 153343038
      {'aut_label': '12A1', 'centralizer': '1458.a1', 'counter': 48, 'group_counter': 107, 'group_order': 17496, 'label': '12C-1', 'order': 12, 'powers': [39, 38], 'representative': 9256391022970532091845044759, 'size': 1458}
  • gps_qchar • Show schema
    • id: 14795576
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.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], 'schur_index': 1}
    • id: 14795587
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.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], 'schur_index': 1}
    • id: 14795598
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.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], 'schur_index': 1}
    • id: 14795609
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.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], 'schur_index': 1}
    • id: 14795613
      {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.1e', 'multiplicity': 2, 'nt': [3, 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, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 14795614
      {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.1f', 'multiplicity': 2, 'nt': [6, 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, -1, -1, -2, -2, 2, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
    • id: 14795615
      {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.1g', 'multiplicity': 2, 'nt': [6, 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, -1, -1, -2, 2, -2, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1], 'schur_index': 1}
    • id: 14795616
      {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.1h', 'multiplicity': 2, 'nt': [6, 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, -1, -1, 2, -2, -2, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 14795617
      {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.2a', 'multiplicity': 1, 'nt': [8, 5], '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, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
    • id: 14795577
      {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.2b', 'multiplicity': 2, 'nt': [24, 4], 'qdim': 4, 'qvalues': [4, -4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, -2, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795578
      {'cdim': 8, 'counter': 11, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.8a', 'multiplicity': 1, 'nt': [9, 14], 'qdim': 8, 'qvalues': [8, 0, 8, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 8, 8, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795579
      {'cdim': 8, 'counter': 12, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.8b', 'multiplicity': 2, 'nt': [24, 565], 'qdim': 16, 'qvalues': [16, 0, 16, -2, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 16, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 16, -8, -8, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795580
      {'cdim': 24, 'counter': 13, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24a', 'multiplicity': 1, 'nt': [27, 415], 'qdim': 24, 'qvalues': [24, 0, 24, 6, -3, -3, -3, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, 6, -3, 6, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795581
      {'cdim': 24, 'counter': 14, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24b', 'multiplicity': 1, 'nt': [27, 951], 'qdim': 24, 'qvalues': [24, 0, -3, -3, 6, -3, -3, -3, -3, -3, -3, 15, 6, -3, -3, -3, -3, -3, -3, -3, 6, -3, 6, 6, -3, -3, 6, -3, 6, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795582
      {'cdim': 24, 'counter': 15, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24c', 'multiplicity': 1, 'nt': [27, 951], 'qdim': 24, 'qvalues': [24, 0, -3, 6, 6, -3, -3, -3, -3, -3, -3, -3, 15, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795583
      {'cdim': 24, 'counter': 16, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24d', 'multiplicity': 1, 'nt': [27, 951], 'qdim': 24, 'qvalues': [24, 0, -3, 15, 6, 6, 6, 6, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795584
      {'cdim': 24, 'counter': 17, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24e', 'multiplicity': 1, 'nt': [36, 2814], 'qdim': 24, 'qvalues': [24, 0, 24, -3, -3, -3, -3, -3, 6, 6, 6, -3, -3, 6, 6, 6, -3, -3, -3, -3, -3, -3, 6, -3, -3, -3, -3, -3, 6, -3, -3, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795585
      {'cdim': 24, 'counter': 18, 'faithful': False, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24f', 'multiplicity': 1, 'nt': [36, 2814], 'qdim': 24, 'qvalues': [24, 0, 24, -3, -3, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, 6, 6, 6, -3, 6, -3, -3, 6, -3, -3, 6, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795586
      {'cdim': 24, 'counter': 19, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24g', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, -9, -9, 9, 3, 3, 3, 6, -3, 3, 3, -6, 9, 0, 0, -3, 0, 6, -6, 0, 6, 6, 0, -3, -6, -3, -3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795588
      {'cdim': 24, 'counter': 20, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24h', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, -9, 9, -9, 3, 3, 3, 6, -3, 3, -6, 3, 0, 9, 0, 6, 0, 6, -6, 0, -3, -3, 0, -3, 3, -3, 6, -6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795589
      {'cdim': 24, 'counter': 21, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24i', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, -6, 3, 3, 0, 0, 9, -3, 6, 0, 0, 0, -6, -6, 3, -3, 3, -3, 9, 3, -3, 6, 3, -3, -9, -3, 6, -9, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795590
      {'cdim': 24, 'counter': 22, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24j', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, 0, 0, 9, -6, 3, 3, -3, 6, -6, -6, 3, 0, 0, 0, 6, 9, 6, 3, -9, -3, -3, -9, 6, 3, -3, -3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795591
      {'cdim': 24, 'counter': 23, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24k', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, 0, 9, 0, 3, -6, 3, -3, 6, -6, 3, -6, 0, 0, 0, -3, -9, 6, 3, 9, 6, -3, -9, -3, 3, 6, -3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795592
      {'cdim': 24, 'counter': 24, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24l', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, 3, -6, 3, 0, 9, 0, -3, 6, 0, 0, 0, -6, 3, -6, -3, 3, -3, -9, 3, 6, -3, 3, -3, 9, 6, -3, -9, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795593
      {'cdim': 24, 'counter': 25, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24m', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, 3, 3, -6, 9, 0, 0, -3, 6, 0, 0, 0, 3, -6, -6, 6, 3, -3, -9, 3, -3, -3, 3, 6, -9, -3, -3, 9, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795594
      {'cdim': 24, 'counter': 26, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24n', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, 3, 3, 3, -9, -9, 9, 6, -3, 9, 0, 0, 3, 3, -6, -3, -6, -3, 0, -6, -3, -3, 3, 6, 0, 6, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795595
      {'cdim': 24, 'counter': 27, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24o', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, 3, 3, 3, -9, 9, -9, 6, -3, 0, 9, 0, 3, -6, 3, 6, -6, -3, 0, 3, -3, -3, -6, -3, 0, -3, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795596
      {'cdim': 24, 'counter': 28, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24p', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, 3, 3, 3, 9, -9, -9, 6, -3, 0, 0, 9, -6, 3, 3, -3, 3, -3, 0, -6, 6, 6, -6, -3, 0, -3, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795597
      {'cdim': 24, 'counter': 29, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24q', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, 9, -9, -9, 3, 3, 3, 6, -3, -6, 3, 3, 0, 0, 9, -3, 0, 6, 3, 0, -3, -3, 0, 6, -6, 6, -3, -6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795599
      {'cdim': 24, 'counter': 30, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24r', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, -3, -3, 9, 0, 0, 3, 3, -6, -3, 6, 3, -6, -6, 0, 0, 0, -3, -9, 6, 3, -9, -3, 6, 9, -3, 3, -3, 6, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795600
      {'cdim': 24, 'counter': 31, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24s', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, 6, -3, -6, -6, 3, 0, 0, 0, -3, -3, -9, -9, 9, 3, 3, 3, -3, -6, -3, 0, 3, -3, -3, 3, -3, 0, 6, 6, 9, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795601
      {'cdim': 24, 'counter': 32, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24t', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, 6, -3, -6, 3, -6, 0, 0, 0, -3, -3, -9, 9, -9, 3, 3, 3, -3, 3, -3, 0, -6, -3, 6, 3, 6, 9, -3, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795602
      {'cdim': 24, 'counter': 33, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24u', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, 6, -3, 0, 0, 0, -6, -6, 3, -3, -3, 3, 3, 3, -9, -9, 9, 6, 0, 6, -6, 0, 6, -3, 9, -3, 3, -3, -3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795603
      {'cdim': 24, 'counter': 34, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24v', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, 6, -3, 0, 0, 0, -6, 3, -6, -3, -3, 3, 3, 3, -9, 9, -9, -3, 0, 6, 3, 9, -3, 6, 0, 6, -6, -3, -3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795604
      {'cdim': 24, 'counter': 35, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24w', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, 6, -3, 0, 0, 0, 3, -6, -6, -3, -3, 3, 3, 3, 9, -9, -9, -3, 9, 6, 3, 0, -3, -3, 0, -3, 3, 6, 6, -6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795605
      {'cdim': 24, 'counter': 36, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24x', 'multiplicity': 1, 'nt': [36, 10388], 'qdim': 24, 'qvalues': [24, 0, -3, 6, -3, 3, -6, -6, 0, 0, 0, -3, -3, 9, -9, -9, 3, 3, 3, 6, 3, -3, 9, 3, 6, -3, -6, -3, 0, -3, -3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795606
      {'cdim': 24, 'counter': 37, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24y', 'multiplicity': 1, 'nt': [36, 10389], 'qdim': 24, 'qvalues': [24, 0, -3, -3, 6, -3, -3, 6, 6, -3, -3, -3, -3, -3, 6, -3, -3, 6, -3, 6, -3, -3, 6, -3, 6, -12, 6, 6, -3, -3, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795607
      {'cdim': 24, 'counter': 38, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24z', 'multiplicity': 1, 'nt': [36, 10389], 'qdim': 24, 'qvalues': [24, 0, -3, -3, 6, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, 6, -12, 6, -3, 6, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795608
      {'cdim': 24, 'counter': 39, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24aa', 'multiplicity': 1, 'nt': [36, 10389], 'qdim': 24, 'qvalues': [24, 0, -3, -3, 6, -3, 6, -3, -3, 6, -3, -3, -3, -3, -3, 6, 6, -3, -3, 6, -3, -3, 6, -3, 6, 6, 6, -3, -3, 6, -12, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795610
      {'cdim': 24, 'counter': 40, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24ab', 'multiplicity': 1, 'nt': [36, 10389], 'qdim': 24, 'qvalues': [24, 0, -3, -3, 6, -3, 6, -3, -3, 6, -3, -3, -3, 6, -3, -3, -3, -3, 6, -12, 6, -3, -3, -3, 6, -3, -3, 6, -3, 6, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795611
      {'cdim': 24, 'counter': 41, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24ac', 'multiplicity': 1, 'nt': [36, 10389], 'qdim': 24, 'qvalues': [24, 0, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, -3, -3, 6, 6, -3, -3, -3, -3, -3, -3, 6, 6, 6, -3, 6, 6, -12, 6, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 14795612
      {'cdim': 24, 'counter': 42, 'faithful': True, 'group': '17496.ec', 'group_order': 17496, 'image': None, 'label': '17496.ec.24ad', 'multiplicity': 1, 'nt': [36, 10389], 'qdim': 24, 'qvalues': [24, 0, -3, -3, 6, 6, -3, -3, -3, -3, 6, -3, -3, -3, 6, -3, -3, 6, -3, 6, 6, -3, -3, -3, -3, 6, -3, -12, -3, 6, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
    • id: 34432130
      {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 17496, 'label': '17496.ec.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]]]}
    • id: 34432141
      {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 8748, 'label': '17496.ec.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 34432152
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    • id: 34432163
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    • id: 34432173
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    • id: 34432174
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    • id: 34432175
      {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 2916, 'label': '17496.ec.1f1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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, 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]]]}
    • id: 34432176
      {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 2916, 'label': '17496.ec.1f2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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, 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]]]}
    • id: 34432177
      {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 2916, 'label': '17496.ec.1g1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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, 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]]]}
    • id: 34432131
      {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 2916, 'label': '17496.ec.1g2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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, 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]]]}
    • id: 34432132
      {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 2916, 'label': '17496.ec.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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, 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]]]}
    • id: 34432133
      {'center': '1.a1', 'center_index': 1, 'center_order': 17496, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.a1', 'kernel_order': 2916, 'label': '17496.ec.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 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, 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]]]}
    • id: 34432134
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    • id: 34432135
      {'center': '4.a1', 'center_index': 4, 'center_order': 4374, 'counter': 14, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '24.11', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 729, 'label': '17496.ec.2b1', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[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]]]}
    • id: 34432136
      {'center': '4.a1', 'center_index': 4, 'center_order': 4374, 'counter': 15, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '24.11', 'image_order': 24, 'indicator': 0, 'kernel': '24.a1', 'kernel_order': 729, 'label': '17496.ec.2b2', 'nt': [24, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[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]]]}
    • id: 34432137
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    • id: 34432138
      {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 17, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '216.160', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ec.8b1', 'nt': [24, 565], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, -1]], [[8, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432139
      {'center': '72.a1', 'center_index': 72, 'center_order': 243, 'counter': 18, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '216.160', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1', 'kernel_order': 81, 'label': '17496.ec.8b2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[8, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[8, 0]], [[8, 1]], [[8, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432140
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    • id: 34432169
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 45, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24aa', 'nt': [36, 10389], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-12, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432170
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    • id: 34432171
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    • id: 34432172
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    • id: 34432142
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    • id: 34432143
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    • id: 34432144
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    • id: 34432145
      {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 23, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.2330', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ec.24e', 'nt': [36, 2814], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432146
      {'center': '1944.a1', 'center_index': 1944, 'center_order': 9, 'counter': 24, 'cyclotomic_n': 1, 'dim': 24, 'faithful': False, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '1944.2330', 'image_order': 1944, 'indicator': 1, 'kernel': '1944.a1', 'kernel_order': 9, 'label': '17496.ec.24f', 'nt': [36, 2814], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[24, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432147
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 25, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24g', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-9, 0]], [[-9, 0]], [[9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[6, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[-6, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432148
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 26, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24h', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-9, 0]], [[9, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[6, 0]], [[-3, 0]], [[3, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[9, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[6, 0]], [[-6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432149
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 27, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24i', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[9, 0]], [[3, 0]], [[-3, 0]], [[6, 0]], [[3, 0]], [[-3, 0]], [[-9, 0]], [[-3, 0]], [[6, 0]], [[-9, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432150
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24j', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[9, 0]], [[6, 0]], [[3, 0]], [[-9, 0]], [[-3, 0]], [[-3, 0]], [[-9, 0]], [[6, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432151
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    • id: 34432153
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    • id: 34432154
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    • id: 34432155
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    • id: 34432156
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    • id: 34432157
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 34, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24p', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432158
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 35, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24q', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[6, 0]], [[-3, 0]], [[-6, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[9, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[6, 0]], [[-3, 0]], [[-6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432159
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 36, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24r', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[9, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-6, 0]], [[-3, 0]], [[6, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-9, 0]], [[6, 0]], [[3, 0]], [[-9, 0]], [[-3, 0]], [[6, 0]], [[9, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[6, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432160
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 37, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24s', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-9, 0]], [[-9, 0]], [[9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-6, 0]], [[-3, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[6, 0]], [[9, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432161
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 38, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24t', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-9, 0]], [[9, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[-6, 0]], [[-3, 0]], [[6, 0]], [[3, 0]], [[6, 0]], [[9, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432162
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 39, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24u', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-9, 0]], [[-9, 0]], [[9, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[9, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432164
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 40, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24v', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[-6, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-9, 0]], [[9, 0]], [[-9, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[3, 0]], [[9, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[6, 0]], [[-6, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432165
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 41, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24w', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[-3, 0]], [[9, 0]], [[6, 0]], [[3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[3, 0]], [[6, 0]], [[6, 0]], [[-6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432166
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 42, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24x', 'nt': [36, 10388], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[3, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[9, 0]], [[-9, 0]], [[-9, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[6, 0]], [[3, 0]], [[-3, 0]], [[9, 0]], [[3, 0]], [[6, 0]], [[-3, 0]], [[-6, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432167
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 43, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24y', 'nt': [36, 10389], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[-12, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 34432168
      {'center': '17496.a1', 'center_index': 17496, 'center_order': 1, 'counter': 44, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '17496.ec', 'group_counter': 107, 'group_order': 17496, 'image': None, 'image_isoclass': '17496.ec', 'image_order': 17496, 'indicator': 1, 'kernel': '17496.a1', 'kernel_order': 1, 'label': '17496.ec.24z', 'nt': [36, 10389], 'q_character': None, 'values': [[[24, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-12, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • gps_subgroup_search • Show schema
    Showing the first 100 of 566 matching records in this table.
    • id: 157301913
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 17496, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '17496.ec.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0', 'R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '17496.ec', 'subgroup_hash': 973806794745079939, 'subgroup_order': 17496, 'subgroup_tex': 'C_3^2\\wr C_3:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 157302024
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 8748, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1', 'C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 115223266166413924, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 157302135
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 5832, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.3.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8308808951802383450, 'subgroup_order': 5832, 'subgroup_tex': 'C_3^6.Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 157302246
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 4374, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2', 'C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8927994121290143594, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^6.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 157302357
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2916, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6218027514413146265, 'subgroup_order': 2916, 'subgroup_tex': 'C_3^6.C_4', 'supersolvable': False, 'sylow': 0}
    • id: 157302435
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 2187, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '17496.ec.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': ['F', 'F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2187.2052', 'subgroup_hash': 6501777776849519009, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^2\\wr C_3', 'supersolvable': True, 'sylow': 3}
    • id: 157302446
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2330', 'subgroup_hash': 2330, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 157302457
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1458, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3', 'D', 'L1', 'D1', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1795', 'subgroup_hash': 1795, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302468
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1458.1109', 'subgroup_hash': 1109, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 157301914
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 157301925
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': True, 'core_order': 729, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'D2', 'C4', 'L2', 'D2', 'C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 157301936
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 243, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.290', 'subgroup_hash': 290, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 157301947
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '729.325', 'subgroup_hash': 325, 'subgroup_order': 729, 'subgroup_tex': 'C_3^5.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 157301958
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 157301969
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 157301980
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 157301991
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.167', 'subgroup_hash': 167, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 157302002
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.167', 'subgroup_hash': 167, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 157302013
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 243, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.146', 'subgroup_hash': 146, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 157302025
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.260', 'subgroup_hash': 260, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302036
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.260', 'subgroup_hash': 260, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302047
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.260', 'subgroup_hash': 260, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302058
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.260', 'subgroup_hash': 260, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302069
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.260', 'subgroup_hash': 260, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302080
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.260', 'subgroup_hash': 260, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302091
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 157302102
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 157302113
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 157302124
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 157302136
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.54.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 157302147
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 157302158
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 157302169
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 243, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.41', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\PSU(3,2)', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302180
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
    • id: 157302191
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
    • id: 157302202
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
    • id: 157302213
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 9, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
    • id: 157302224
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.51', 'subgroup_hash': 51, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302235
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.13', 'subgroup_hash': 13, 'subgroup_order': 243, 'subgroup_tex': 'C_3^3:C_9', 'supersolvable': True, 'sylow': 0}
    • id: 157302247
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 81, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
    • id: 157302258
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 9, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
    • id: 157302269
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.51', 'subgroup_hash': 51, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302280
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.13', 'subgroup_hash': 13, 'subgroup_order': 243, 'subgroup_tex': 'C_3^3:C_9', 'supersolvable': True, 'sylow': 0}
    • id: 157302291
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.72.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.38', 'subgroup_hash': 38, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302302
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.160', 'subgroup_hash': 160, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 157302313
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.11', 'subgroup_hash': 11, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 157302324
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.11', 'subgroup_hash': 11, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 157302335
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.11', 'subgroup_hash': 11, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 157302346
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 157302358
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302369
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302380
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.e3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302391
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302402
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.f2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302413
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302424
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302432
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302433
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302434
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.j2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302436
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.j3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302437
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302438
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.k2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302439
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302440
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.l2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302441
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302442
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.m2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302443
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302444
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.n2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302445
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302447
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302448
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302449
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302450
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302451
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302452
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302453
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.v1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302454
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.w1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302455
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 81, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.x1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302456
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302458
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.z1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302459
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.z2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302460
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.z3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302461
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.z4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.z4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302462
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.ba1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302463
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.ba2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ba2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302464
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.ba3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ba3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302465
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bb1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302466
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bc1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302467
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bc2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302469
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bc3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302470
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bc4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302471
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bc5', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302472
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bc6', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bc6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302473
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bd1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302474
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bd2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bd2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302475
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.bd3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bd3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302476
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.be1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302477
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.be2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157302478
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.be3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 157301915
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '17496.ec', 'ambient_counter': 107, 'ambient_order': 17496, 'ambient_tex': 'C_3^2\\wr C_3:Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '17496.ec.108.be4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 566 matching records in this table.
    • id: 157301913
      {'ambient': '17496.ec', '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': '17496.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '3.a1', '9.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9906, 6562, 9761, 5968], 'generators': [2849517334059285, 2267507354388480, 324885, 4615839911531101360447237799, 112435075062505589522013479, 3228220166063390033219633685, 33014302651624106797388232, 47882431127126422787571329, 174793, 2094763166518465308969156132], 'label': '17496.ec.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '4608.fx'}
    • id: 157301914
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['2.a1', '9.a1'], 'contains': ['36.c1', '54.b1', '162.a1'], 'core': '72.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9885, -1, 9272, -1], 'generators': [2849517334059285, 2267507354388480, 4615839911530846264795775399, 3228220166063390033219633685, 33014302651624106797388232, 112435075062505589522195948, 2094763166518465308969156132], 'label': '17496.ec.18.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.a1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '1944.2330'}
    • id: 157301915
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '108.be4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['36.e1', '36.f1'], 'contains': ['216.bf4', '324.bd1', '324.bf1', '324.bf5', '324.bj3', '324.bj9', '324.bm1', '324.bm5', '324.bn1', '324.bn2', '324.bn3', '324.bn6', '324.bo1', '324.bo2', '324.bp1', '324.bw1', '324.bx1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1296, 'diagramx': [6582, -1, 6498, -1], 'generators': [3228220166063390033219386121, 1646776838392686240813847332, 112435075062505589522013479, 3228220166065479540661533732, 2094763166517755155164295680], 'label': '17496.ec.108.be4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.be4', 'old_label': '108.be4', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be4', 'subgroup_fusion': None, 'weyl_group': '162.54'}
    • id: 157301916
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['36.d1', '36.f1'], 'contains': ['216.bg1', '324.bf1', '324.bf4', '324.bf5', '324.bf7', '324.bk1', '324.bk2', '324.bl1', '324.bl2', '324.bl3', '324.bs1', '324.bv1', '324.bv2', '324.bv3', '324.bv4', '324.cc1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [7135, -1, 5876, -1], 'generators': [3228220166062885089288269321, 112435075062505589522013479, 513163763439777541426406400, 2094763166516995115581614793, 1258350440042503593257779544], 'label': '17496.ec.108.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bf1', 'old_label': '108.bf1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
    • id: 157301917
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['36.e1', '36.f1'], 'contains': ['216.bh1', '324.bf6', '324.bg1', '324.bl1', '324.bl2', '324.bn2', '324.bn5', '324.br1', '324.bt3', '324.bu1', '324.bu3', '324.bv2', '324.bv4', '324.bw1', '324.bx1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [5876, -1, 5806, -1], 'generators': [112435075062505589522013479, 174793, 3228220166065479540661533732, 2094763166516995115581614793, 840788568360280067521768393], 'label': '17496.ec.108.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bg1', 'old_label': '108.bg1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1', 'subgroup_fusion': None, 'weyl_group': '162.54'}
    • id: 157301918
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '108.bg2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['36.e1', '36.f1'], 'contains': ['216.bh2', '324.bf2', '324.bf3', '324.bg2', '324.bl1', '324.bl2', '324.bl3', '324.bn1', '324.bn3', '324.bn4', '324.bn6', '324.br1', '324.bt1', '324.bt2', '324.bu2', '324.bu3', '324.bv1', '324.bv3', '324.bv4', '324.bw1', '324.bx1', '324.bx2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [6019, -1, 6014, -1], 'generators': [3228220166063390033219386121, 1646776838392686240813847332, 112435075062505589522013479, 3228220166065479540661533732, 2094763166516995115581614793], 'label': '17496.ec.108.bg2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.bg2', 'old_label': '108.bg2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg2', 'subgroup_fusion': None, 'weyl_group': '162.54'}
    • id: 157301919
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.f1', '54.e1'], 'contains': ['216.bi1', '324.bq1', '324.bs1', '324.bx1', '324.bx2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [5353, -1, 4769, -1], 'generators': [3228220166062885089288269321, 324885, 112435075062505589522013479, 174793, 2094763166516995115581614793], 'label': '17496.ec.108.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '108.bh1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
    • id: 157301920
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['36.d1', '54.f1'], 'contains': ['216.bj1', '324.bz1', '324.bz2', '324.ca2', '324.ca3', '324.ca4', '324.cc1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 486, 'diagramx': [9532, -1, 8804, -1], 'generators': [3228220166062885089288269321, 112435075062505589522013479, 2516538717431153201374234121, 2094763166516995115581614793, 840788568360280067521768393], 'label': '17496.ec.108.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.f1', 'old_label': '108.bi1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1', 'subgroup_fusion': None, 'weyl_group': '324.164'}
    • id: 157301921
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.a1', '81.a1'], 'contains': ['324.c1', '486.a1', '1458.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [9919, -1, 9186, -1], 'generators': [6291590060603434910342917799, 3228220166063390033219633685, 33014302651624106797388232, 112435075063470840937847834, 2094763166518465308969156132], 'label': '17496.ec.162.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.a1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 157301922
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.h1', '72.l1', '108.x1'], 'contains': ['648.s1', '648.v1', '648.bc1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [207, 3209, 652, 4593], 'generators': [2849517334059285, 2267507354388480, 3228220166063390033219633685, 2094763166518465308969156132], 'label': '17496.ec.216.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': ['24.a1', '72.a1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '24.11'}
    • id: 157301923
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '72.e1', '108.e1'], 'contains': ['648.a1', '648.a2', '648.d1', '648.e1', '648.e2', '648.f1', '648.o1', '648.p1', '648.w1', '648.y1', '648.bi1', '648.bi2', '648.bi3', '648.bi4', '648.bm1', '648.bm2', '648.bm3', '648.bm4', '648.bm5', '648.bm6', '648.bm7', '648.bo1', '648.bq1', '648.bq2', '648.cd1', '648.cd2', '648.cd3', '648.cg1', '648.cg2', '648.cg3', '648.cg4', '648.cg5', '648.cg6'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2782, -1, 2895, -1], 'generators': [504943931211562, 504943931116800, 3228220166065479540661533732, 2094763166518465308969156132], 'label': '17496.ec.216.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.b1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301924
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.b2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '72.e1', '108.e2'], 'contains': ['648.a1', '648.d1', '648.e1', '648.e2', '648.f2', '648.o2', '648.p1', '648.w1', '648.y1', '648.y2', '648.bi1', '648.bi2', '648.bi5', '648.bi6', '648.bm1', '648.bm2', '648.bm8', '648.bm9', '648.bm10', '648.bm11', '648.bm12', '648.bo2', '648.bq3', '648.bq4', '648.cd1', '648.cd2', '648.cd3', '648.cd4', '648.cg1', '648.cg2', '648.cg3', '648.cg7', '648.cg8', '648.cg9'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3064, -1, 2932, -1], 'generators': [513163763438812819706695680, 3228220166064769884902215680, 1134035330304344, 2094763166518465308969156132], 'label': '17496.ec.216.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.b2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301925
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.a1'], 'contains': ['72.b1', '72.c1', '72.d1', '72.e1', '72.h1', '72.i1'], 'core': '24.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1748, 4298, 2306, 6365], 'generators': [2849517334059285, 2267507354388480, 324885, 3228220166063390033219633685, 174793, 2094763166518465308969156132], 'label': '17496.ec.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['216.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '24.11'}
    • id: 157301926
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.b3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '72.e1', '108.e3'], 'contains': ['648.a1', '648.a2', '648.d1', '648.e1', '648.f2', '648.o1', '648.p1', '648.w1', '648.y1', '648.y2', '648.bi3', '648.bi5', '648.bi6', '648.bi7', '648.bm3', '648.bm4', '648.bm5', '648.bm8', '648.bm9', '648.bm13', '648.bm14', '648.bo3', '648.bq5', '648.bq6', '648.cd1', '648.cd2', '648.cd4', '648.cg1', '648.cg2', '648.cg4', '648.cg5', '648.cg7', '648.cg10'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3005, -1, 2859, -1], 'generators': [3228220166064769884902215680, 1134035330091562, 3228220166063390033219447490, 2094763166518465308969156132], 'label': '17496.ec.216.b3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.b3', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301927
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.c1', '72.h1', '108.f1'], 'contains': ['648.g1', '648.g2', '648.j1', '648.o1', '648.o2', '648.s1', '648.x1', '648.x2', '648.bg1', '648.bg2', '648.bj1', '648.bj2', '648.bk1', '648.bk2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [760, -1, 1609, -1], 'generators': [2849517334059285, 513163763439777541426501162, 3228220166064355282675774762, 2094763166518465308969156132], 'label': '17496.ec.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.c1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301928
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.c2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '72.h1', '108.f2'], 'contains': ['648.a1', '648.a2', '648.c1', '648.h1', '648.p1', '648.s1', '648.bg1', '648.bg2', '648.bj1', '648.bj2', '648.bk1', '648.bk2', '648.bs1', '648.bu1', '648.cb1', '648.ce1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1429, -1, 1977, -1], 'generators': [2094763166519589566954878485, 1884795613975332, 3228220166063390033219633685, 1134035330304344], 'label': '17496.ec.216.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.c2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301929
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.b1', '72.i1', '108.g1'], 'contains': ['648.b1', '648.d1', '648.k1', '648.r1', '648.w1', '648.bh1', '648.bh2', '648.bn1', '648.bn2', '648.cc1', '648.cc2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4514, -1, 2675, -1], 'generators': [2849517334059285, 1646776838392686240813847332, 3228220166063390033219633685, 2094763166518465308969235544], 'label': '17496.ec.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.d1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301930
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.b1', '72.d1', '72.e1', '108.h1'], 'contains': ['648.b1', '648.e1', '648.e2', '648.f1', '648.f2', '648.q1', '648.y1', '648.y2', '648.bi1', '648.bi2', '648.bi3', '648.bi4', '648.bi5', '648.bi6', '648.bi7', '648.bo1', '648.bo2', '648.bo3', '648.bt1', '648.cd1', '648.cd2', '648.cd3', '648.cd4'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1410, -1, 2343, -1], 'generators': [2849517334059285, 1646776838392686240813847332, 3228220166063390033219633685, 1134035330091562], 'label': '17496.ec.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.e1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301931
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['72.b1', '72.d1', '72.h1', '108.i1'], 'contains': ['648.a1', '648.a2', '648.b1', '648.h1', '648.p1', '648.v1', '648.bg1', '648.bg2', '648.bj1', '648.bj2', '648.bu1', '648.bv1', '648.ce1', '648.cf1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2075, -1, 1646, -1], 'generators': [2267507354388480, 3228220166062885089288269321, 2094763166518129150911744344, 3228220166063390033219447490], 'label': '17496.ec.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.f1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301932
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.c1', '72.e1', '108.j1'], 'contains': ['648.c1', '648.e2', '648.f1', '648.x1', '648.y2', '648.bm10', '648.bm11', '648.bm13', '648.bq1', '648.bx1', '648.cg4', '648.cg8'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1419, -1, 2527, -1], 'generators': [513163763437688063675389890, 3228220166065152596642611544, 1134035330304344, 2094763166518465308969156132], 'label': '17496.ec.216.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.g1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301933
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.g2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.c1', '72.e1', '108.j2'], 'contains': ['648.c1', '648.e1', '648.f2', '648.x1', '648.y1', '648.bm3', '648.bm4', '648.bm6', '648.bm12', '648.bq3', '648.bq5', '648.bx2', '648.cg5', '648.cg6', '648.cg9', '648.cg10'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1769, -1, 2969, -1], 'generators': [513163763437688063675389890, 3228220166065152596642611544, 513163763437688063675479332, 2094763166518465308969156132], 'label': '17496.ec.216.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.g2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301934
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.g3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '72.e1', '108.j3'], 'contains': ['648.c1', '648.e1', '648.e2', '648.f1', '648.f2', '648.x2', '648.y1', '648.y2', '648.bm1', '648.bm2', '648.bm5', '648.bm7', '648.bm8', '648.bm9', '648.bm14', '648.bq2', '648.bq4', '648.bq6', '648.bx3', '648.cg1', '648.cg2', '648.cg3', '648.cg7'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1669, -1, 2822, -1], 'generators': [513163763437688063675389890, 3228220166065152596642611544, 513163763438812819706744085, 2094763166518465308969156132], 'label': '17496.ec.216.g3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.g3', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301935
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.b1', '72.c1', '72.i1', '108.k1'], 'contains': ['648.a2', '648.d1', '648.e1', '648.f1', '648.f2', '648.h1', '648.k1', '648.o2', '648.bh1', '648.bl1', '648.bl2', '648.bl3', '648.bl4', '648.bn1', '648.bp1', '648.bp2', '648.bp3', '648.bp4', '648.br1', '648.bw1', '648.by1', '648.by2', '648.cc1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [3442, -1, 2454, -1], 'generators': [3228220166064769884902215680, 1134035330091562, 1134035330304344, 2094763166518465308969156132], 'label': '17496.ec.216.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.h1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301936
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '12.b1'], 'contains': ['72.a1', '72.f1', '72.h1', '72.j1', '72.l1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [154, -1, 510, -1], 'generators': [2849517334059285, 2267507354388480, 3228220166063390033219633685, 5016573249304414543082179200, 174793, 2094763166518465308969156132], 'label': '17496.ec.24.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '24.b1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '486.146'}
    • id: 157301937
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.h2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '72.i1', '108.k2'], 'contains': ['648.a1', '648.d1', '648.e1', '648.e2', '648.f1', '648.f2', '648.h1', '648.k1', '648.o1', '648.bh2', '648.bl1', '648.bl2', '648.bl3', '648.bl4', '648.bn2', '648.bp1', '648.bp2', '648.bp3', '648.bp4', '648.bp5', '648.bp6', '648.bp7', '648.br2', '648.bw2', '648.bw3', '648.by3', '648.by4', '648.cc2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2872, -1, 2490, -1], 'generators': [513163763438812819706695680, 3228220166065479540661305600, 3228220166064769884902215680, 2094763166518465308969156132], 'label': '17496.ec.216.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.h2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301938
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '72.d1', '72.e1', '108.l1'], 'contains': ['648.a1', '648.e1', '648.f1', '648.g1', '648.i1', '648.l1', '648.p1', '648.y1', '648.y2', '648.bi3', '648.bi4', '648.bi7', '648.bm5', '648.bm7', '648.bm10', '648.bm11', '648.bm12', '648.bm14', '648.bo1', '648.bo3', '648.bq2', '648.bq3', '648.bq6', '648.bt1', '648.bx1', '648.bx3'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1241, -1, 2306, -1], 'generators': [3228220166065479540661613144, 3228220166064769884902215680, 3228220166064355282675956480, 2094763166518465308969156132], 'label': '17496.ec.216.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.i1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301939
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.i2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.c1', '72.d1', '72.e1', '108.l2'], 'contains': ['648.a1', '648.a2', '648.e1', '648.e2', '648.f2', '648.g2', '648.i1', '648.l1', '648.p1', '648.y1', '648.y2', '648.bi1', '648.bi2', '648.bi5', '648.bi6', '648.bm1', '648.bm2', '648.bm3', '648.bm4', '648.bm6', '648.bm8', '648.bm9', '648.bm13', '648.bo1', '648.bo2', '648.bo3', '648.bq1', '648.bq2', '648.bq4', '648.bq5', '648.bq6', '648.bt1', '648.bx2', '648.bx3'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [1204, -1, 2380, -1], 'generators': [513163763438812819706695680, 3228220166064769884902215680, 174793, 2094763166518465308969156132], 'label': '17496.ec.216.i2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.i2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301940
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.c1', '72.i1', '108.m1'], 'contains': ['648.c1', '648.d1', '648.j1', '648.k1', '648.l1', '648.w1', '648.bl1', '648.bl2', '648.bl3', '648.bp1', '648.bp2', '648.bp5', '648.bw1', '648.bw2', '648.bw3'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2361, -1, 2638, -1], 'generators': [513163763437688063675389890, 3228220166065152596642611544, 513163763439777541426501162, 2094763166518465308969156132], 'label': '17496.ec.216.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.j1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301941
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.j2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.c1', '72.i1', '108.m2'], 'contains': ['648.c1', '648.d1', '648.i1', '648.j1', '648.m1', '648.bl4', '648.bp3', '648.bp4', '648.bp6', '648.bp7', '648.bz1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1632, -1, 2196, -1], 'generators': [3228220166065152596642611544, 324885, 174793, 2094763166518465308969156132], 'label': '17496.ec.216.j2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.j2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301942
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '72.d1', '72.i1', '108.n1'], 'contains': ['648.a1', '648.e1', '648.f1', '648.f2', '648.g2', '648.h1', '648.l1', '648.m1', '648.bh2', '648.bn2', '648.bp1', '648.bp2', '648.bp3', '648.bp4', '648.bw1', '648.bw2', '648.bw3', '648.by3', '648.by4', '648.bz1', '648.ca1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [905, -1, 2122, -1], 'generators': [513163763438812819706695680, 3228220166064769884902215680, 513163763438812819706744085, 2094763166518465308969156132], 'label': '17496.ec.216.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.k1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301943
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.k2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['72.c1', '72.d1', '72.i1', '108.n2'], 'contains': ['648.a2', '648.e2', '648.f2', '648.g1', '648.h1', '648.l1', '648.m1', '648.bh1', '648.bn1', '648.bp5', '648.bp6', '648.bp7', '648.bw2', '648.bw3', '648.by1', '648.by2', '648.bz1', '648.ca2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [770, -1, 1940, -1], 'generators': [3228220166064769884902215680, 1134035330091562, 3228220166064355282675956480, 2094763166518465308969156132], 'label': '17496.ec.216.k2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.k2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301944
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '108.a1'], 'contains': ['648.n1', '648.t1', '648.u1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [96, -1, 365, -1], 'generators': [1884795613975332, 5016573249304414543082179200, 174793, 2094763166518465308969156132], 'label': '17496.ec.216.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '216.l1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 157301945
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1', '72.h1', '108.o1'], 'contains': ['648.g1', '648.g2', '648.n1', '648.q1', '648.v1', '648.bs1', '648.bu1', '648.bv1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [490, -1, 762, -1], 'generators': [1884795613975332, 174793, 3228220166065479540661533732, 2094763166518465308969156132], 'label': '17496.ec.216.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.m1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301946
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.d1', '72.i1', '108.p1'], 'contains': ['648.b1', '648.i1', '648.l1', '648.m1', '648.n1', '648.br1', '648.br2', '648.by1', '648.by2', '648.by3', '648.by4', '648.ca1', '648.ca2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [508, -1, 1314, -1], 'generators': [2849517334059285, 1646776838392686240813847332, 324885, 3228220166063390033219633685], 'label': '17496.ec.216.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.n1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301947
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1'], 'contains': ['72.g1', '72.h1', '72.k1', '72.l1'], 'core': '216.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [60, -1, 254, -1], 'generators': [2849517334059285, 2267507354388480, 5016573249304209333092265600, 3228220166063390033219633685, 174793, 2094763166518465308969156132], 'label': '17496.ec.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '24.c1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '243.37'}
    • id: 157301948
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.f1', '108.b1'], 'contains': ['648.r1', '648.t1', '648.u1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [114, -1, 433, -1], 'generators': [1884795613975332, 6274917809021630340030326400, 3228220166063390033219447490, 2094763166518465308969156132], 'label': '17496.ec.216.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '216.o1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 157301949
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '72.h1', '108.q1'], 'contains': ['648.o1', '648.o2', '648.q1', '648.r1', '648.v1', '648.cb1', '648.ce1', '648.cf1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3414, -1, 1535, -1], 'generators': [1884795613975332, 3228220166065479540661533732, 3228220166063390033219447490, 2094763166518465308969156132], 'label': '17496.ec.216.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.p1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301950
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.j1', '108.c1'], 'contains': ['648.x2', '648.z1', '648.ba1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [48, -1, 209, -1], 'generators': [3228220166063645128870909890, 5016573249304414543082179200, 1134035330304344, 2094763166518465308969156132], 'label': '17496.ec.216.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '216.q1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 157301951
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.e1', '72.h1', '72.i1', '108.r1'], 'contains': ['648.a1', '648.a2', '648.b1', '648.c1', '648.g1', '648.g2', '648.o1', '648.o2', '648.bb1', '648.bc1', '648.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [395, -1, 1001, -1], 'generators': [2849517334059285, 3228220166063390033219633685, 174793, 2094763166518465308969156132], 'label': '17496.ec.216.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.r1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301952
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.i1', '108.s1'], 'contains': ['648.e1', '648.e2', '648.i1', '648.w1', '648.bb1', '648.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [440, -1, 1462, -1], 'generators': [324885, 3228220166063390033219633685, 2849517333873090, 2094763166518465308969156132], 'label': '17496.ec.216.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.s1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301953
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.e1', '72.i1', '108.t1'], 'contains': ['648.d1', '648.f1', '648.f2', '648.l1', '648.bb1', '648.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [404, -1, 1498, -1], 'generators': [2594451373438485, 324885, 3228220166063390033219633685, 2094763166518465308969156132], 'label': '17496.ec.216.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.t1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301954
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '72.g1', '72.h1', '72.i1', '108.u1'], 'contains': ['648.h1', '648.j1', '648.n1', '648.r1', '648.bb1', '648.bc1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [166, -1, 689, -1], 'generators': [1884795613975332, 3228220166063390033219633685, 174793, 2094763166518465308969156132], 'label': '17496.ec.216.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.u1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 157301955
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1', '108.v1'], 'contains': ['648.k1', '648.m1', '648.bb1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1850, -1, 1278, -1], 'generators': [324885, 3228220166063390033219633685, 174793, 2094763166518465308969156132], 'label': '17496.ec.216.v1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.v1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1', 'subgroup_fusion': None, 'weyl_group': '8.4'}
    • id: 157301956
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.e1', '72.h1', '72.j1', '72.k1', '108.w1'], 'contains': ['648.p1', '648.q1', '648.x1', '648.x2', '648.bc1', '648.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [154, -1, 725, -1], 'generators': [1884795613975332, 3228220166063390033219633685, 2267507354189321, 2094763166518465308969156132], 'label': '17496.ec.216.w1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '216.w1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 157301957
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.f1', '72.j1', '108.d1'], 'contains': ['648.t1', '648.z1', '648.bc1', '648.be1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [72, -1, 287, -1], 'generators': [2849517334059285, 3228220166063390033219633685, 5016573249306298808883868800, 2094763166518465308969156132], 'label': '17496.ec.216.x1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '216.x1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1', 'subgroup_fusion': None, 'weyl_group': '162.40'}
    • id: 157301958
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['54.a1', '243.a1', '243.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9849, -1, 9887, -1], 'generators': [112435075063470840938075215, 324885, 3228220166063390033219633685, 33014302651624106797388232, 47882431127126422787571329, 174793, 2094763166518465308969156132], 'label': '17496.ec.27.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
    • id: 157301959
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1', '72.j1', '72.l1'], 'contains': ['648.u1', '648.ba1', '648.bc1', '648.bf1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [29, -1, 137, -1], 'generators': [1884795613975332, 3228220166063390033219633685, 5016573249304414543082179200, 2094763166518465308969156132], 'label': '17496.ec.216.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1', 'old_label': '216.y1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
    • id: 157301960
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.y2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.g1', '72.k1', '72.l1'], 'contains': ['648.bc1', '648.bf1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [13, -1, 75, -1], 'generators': [2849517334059285, 3228220166063390033219633685, 5016573249304414543082179200, 2094763166518465308969156132], 'label': '17496.ec.216.y2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '216.y2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y2', 'subgroup_fusion': None, 'weyl_group': '81.12'}
    • id: 157301961
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.e1', '108.y1'], 'contains': ['648.y1', '648.y2', '648.bd1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4071, -1, 1903, -1], 'generators': [2267507354340132, 3228220166063390033219633685, 760039582855680, 2094763166518465308969156132], 'label': '17496.ec.216.z1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '216.z1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.z1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
    • id: 157301962
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.b1', '72.c1', '108.z1'], 'contains': ['648.bi1', '648.bi2', '648.bi5', '648.bj1', '648.bl1', '648.bl2', '648.bm7', '648.bm10', '648.bm11', '648.bm14', '648.bn2', '648.bp6', '648.bp7', '648.cc1', '648.cc2', '648.cd1', '648.cd4', '648.ce1', '648.cg1', '648.cg3', '648.cg5'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4443, -1, 3153, -1], 'generators': [3228220166065152596642611544, 2900600827630409708907704085, 1646776838392686240813757890, 2094763166518129150911744344], 'label': '17496.ec.216.ba1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.ba1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301963
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.ba2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.b1', '72.c1', '108.z2'], 'contains': ['648.bh1', '648.bh2', '648.bi1', '648.bi4', '648.bj2', '648.bl1', '648.bl4', '648.bm8', '648.bm13', '648.bo1', '648.bp1', '648.cc2', '648.cd1', '648.cd4', '648.ce1', '648.cg1', '648.cg2', '648.cg6', '648.cg9'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4433, -1, 3227, -1], 'generators': [3228220166065152596642611544, 2516538717431153201374234121, 513163763439777541426406400, 2094763166518129150911744344], 'label': '17496.ec.216.ba2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.ba2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301964
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.ba3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '108.z3'], 'contains': ['648.bh1', '648.bh2', '648.bi1', '648.bi5', '648.bi7', '648.bj1', '648.bj2', '648.bl2', '648.bl3', '648.bl4', '648.bm1', '648.bm5', '648.bm6', '648.bm12', '648.bo2', '648.bo3', '648.bp2', '648.bp5', '648.cc1', '648.cc2', '648.cd1', '648.cd2', '648.cd3', '648.ce1', '648.cg2', '648.cg3', '648.cg4', '648.cg5', '648.cg7', '648.cg8', '648.cg10'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [4258, -1, 3448, -1], 'generators': [3228220166065152596642611544, 2516538717431153201374234121, 2094763166518129150911744344, 840788568360280067521768393], 'label': '17496.ec.216.ba3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.ba3', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301965
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.ba4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '108.z4'], 'contains': ['648.bi1', '648.bi3', '648.bi4', '648.bi5', '648.bi6', '648.bi7', '648.bj2', '648.bl1', '648.bl2', '648.bl3', '648.bm2', '648.bm3', '648.bm4', '648.bm9', '648.bn1', '648.bn2', '648.bp3', '648.bp4', '648.cc1', '648.cc2', '648.cd1', '648.cd2', '648.cd3', '648.ce1', '648.cg1', '648.cg3', '648.cg4', '648.cg7', '648.cg9'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [4277, -1, 3263, -1], 'generators': [3228220166065152596642611544, 513163763439777541426501162, 2516538717431153201374384932, 2094763166518129150911744344], 'label': '17496.ec.216.ba4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.ba4', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba4', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301966
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '108.ba1'], 'contains': ['648.bg1', '648.bg2', '648.bh2', '648.bi3', '648.bl1', '648.bl2', '648.bl4', '648.bm1', '648.bm2', '648.bm3', '648.bm6', '648.bm8', '648.bm9', '648.bm10', '648.bm13', '648.bn1', '648.bo1', '648.bo3', '648.bp1', '648.bp3', '648.bp4', '648.bp5', '648.bq2', '648.bq5', '648.bw1', '648.cb1', '648.cc2', '648.cd3', '648.cd4', '648.cg2', '648.cg3', '648.cg5', '648.cg7', '648.cg8', '648.cg9'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3771, -1, 3190, -1], 'generators': [1258350440042503593257566762, 2900600827630409708907704085, 3228220166065479540661533732, 2094763166517755155164295680], 'label': '17496.ec.216.bb1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bb1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301967
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bb2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '108.ba2'], 'contains': ['648.bg1', '648.bh2', '648.bi2', '648.bi6', '648.bl1', '648.bl2', '648.bl3', '648.bl4', '648.bm3', '648.bm4', '648.bm5', '648.bm7', '648.bm8', '648.bm12', '648.bm13', '648.bm14', '648.bn2', '648.bo2', '648.bp2', '648.bp3', '648.bp5', '648.bp6', '648.bq3', '648.bq4', '648.bw2', '648.cb1', '648.cc1', '648.cd3', '648.cd4', '648.cg2', '648.cg3', '648.cg4', '648.cg6', '648.cg7', '648.cg9'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3899, -1, 3374, -1], 'generators': [324885, 3228220166065479540661533732, 2094763166517755155164295680, 1258350440042503593257779544], 'label': '17496.ec.216.bb2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bb2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301968
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bb3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '108.ba3'], 'contains': ['648.bg1', '648.bg2', '648.bh1', '648.bi2', '648.bi6', '648.bl1', '648.bl3', '648.bl4', '648.bm1', '648.bm2', '648.bm4', '648.bm5', '648.bm6', '648.bm9', '648.bm11', '648.bm12', '648.bn2', '648.bo1', '648.bo3', '648.bp1', '648.bp2', '648.bp4', '648.bp7', '648.bq1', '648.bq6', '648.bw3', '648.cb1', '648.cc2', '648.cd2', '648.cg1', '648.cg2', '648.cg4', '648.cg5', '648.cg9', '648.cg10'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [3679, -1, 3116, -1], 'generators': [1258350440042503593257566762, 3228220166065479540661533732, 2094763166517755155164295680, 3228220166063390033219447490], 'label': '17496.ec.216.bb3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bb3', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301969
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '9.a1'], 'contains': ['54.b1', '243.a1', '243.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9936, -1, 9836, -1], 'generators': [2849517334059285, 2267507354388480, 3228220166063390033219633685, 112435075062505589521921919, 47882431127126422787571329, 33014302651624106797526800, 2094763166518465308969156132], 'label': '17496.ec.27.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '27.b1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '1944.2330'}
    • id: 157301970
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.b1', '72.d1', '108.bb1'], 'contains': ['648.bh1', '648.bh2', '648.bi2', '648.bi3', '648.bi6', '648.br1', '648.br2', '648.bv1', '648.cd1', '648.cf1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [4122, -1, 2233, -1], 'generators': [3228220166063390033219386121, 3228220166062885089288269321, 2094763166516995115581614793, 1258350440042503593257779544], 'label': '17496.ec.216.bc1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bc1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bc1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301971
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '108.bc1'], 'contains': ['648.bk1', '648.bk2', '648.bl4', '648.bm2', '648.bm4', '648.bm5', '648.bm6', '648.bm7', '648.bm11', '648.bp1', '648.bp5', '648.bp6', '648.bp7', '648.bq1', '648.bq4', '648.bw1', '648.bx1', '648.bx3', '648.cg5', '648.cg7', '648.cg9'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4803, -1, 3006, -1], 'generators': [324885, 3228220166064769884902215680, 513163763439777541426501162, 2094763166518129150911744344], 'label': '17496.ec.216.bd1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bd1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301972
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bd2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.c1', '108.bc2'], 'contains': ['648.bk1', '648.bk2', '648.bl1', '648.bl2', '648.bl3', '648.bm1', '648.bm3', '648.bm5', '648.bm6', '648.bm9', '648.bm11', '648.bm12', '648.bp3', '648.bp4', '648.bp6', '648.bq1', '648.bq2', '648.bq3', '648.bq4', '648.bq5', '648.bq6', '648.bw1', '648.bw2', '648.bw3', '648.cg1', '648.cg2', '648.cg4', '648.cg5', '648.cg6', '648.cg7', '648.cg8'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [4964, -1, 3300, -1], 'generators': [2094763166518465308968928000, 324885, 3228220166064769884902215680, 2094763166518129150911744344], 'label': '17496.ec.216.bd2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bd2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301973
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bd3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.c1', '108.bc3'], 'contains': ['648.bk1', '648.bk2', '648.bl4', '648.bm1', '648.bm2', '648.bm3', '648.bm4', '648.bm8', '648.bm9', '648.bm10', '648.bm12', '648.bm13', '648.bm14', '648.bp1', '648.bp2', '648.bp3', '648.bp4', '648.bp5', '648.bq2', '648.bq3', '648.bq5', '648.bq6', '648.bw2', '648.bw3', '648.bx2', '648.bx3', '648.cg1', '648.cg3', '648.cg4', '648.cg5', '648.cg9'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [5052, -1, 3079, -1], 'generators': [3228220166064769884902215680, 2516538717431153201374234121, 1646776838392686240813757890, 2094763166518129150911744344], 'label': '17496.ec.216.bd3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bd3', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301974
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bd4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '108.bc4'], 'contains': ['648.bk1', '648.bl2', '648.bl3', '648.bm3', '648.bm7', '648.bm8', '648.bm13', '648.bp4', '648.bp7', '648.bq1', '648.bq2', '648.bq3', '648.bq4', '648.bw1', '648.bw3', '648.cg2', '648.cg3', '648.cg9', '648.cg10'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [4925, -1, 3337, -1], 'generators': [1646776838392686240813847332, 324885, 3228220166064769884902215680, 2094763166518129150911744344], 'label': '17496.ec.216.bd4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bd4', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd4', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301975
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bd5', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '108.bc5'], 'contains': ['648.bk1', '648.bl1', '648.bl2', '648.bm1', '648.bm2', '648.bm4', '648.bm5', '648.bm12', '648.bm13', '648.bz1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5436, -1, 3411, -1], 'generators': [513163763439777541426501162, 2516538717431153201374384932, 3228220166065479540661533732, 2094763166518129150911744344], 'label': '17496.ec.216.bd5', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '216.bd5', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd5', 'subgroup_fusion': None, 'weyl_group': '4.1'}
    • id: 157301976
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bd6', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['72.c1', '108.bc6'], 'contains': ['648.bk2', '648.bl3', '648.bm6', '648.bm8', '648.bm10', '648.bm14', '648.bz1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5421, -1, 3043, -1], 'generators': [840788568360280067521870080, 3228220166064769884902215680, 2516538717431153201374384932, 2094763166518129150911744344], 'label': '17496.ec.216.bd6', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '216.bd6', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd6', 'subgroup_fusion': None, 'weyl_group': '4.1'}
    • id: 157301977
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '72.d1', '108.bd1'], 'contains': ['648.bh2', '648.bi1', '648.bi2', '648.bi4', '648.bi6', '648.bj1', '648.bj2', '648.bm2', '648.bm3', '648.bm5', '648.bm6', '648.bm9', '648.bm10', '648.bm13', '648.bn1', '648.bn2', '648.bo2', '648.bo3', '648.bp1', '648.bp2', '648.bp4', '648.bp7', '648.bq2', '648.bq3', '648.bq4', '648.bq5', '648.br1', '648.bt1', '648.bu1', '648.bw2', '648.by3', '648.by4', '648.cd2', '648.cd3', '648.cd4', '648.ce1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2612, -1, 2711, -1], 'generators': [3228220166065152596642611544, 174793, 2094763166518129150911744344, 840788568360280067521768393], 'label': '17496.ec.216.be1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.be1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301978
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.be2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '72.d1', '108.bd2'], 'contains': ['648.bh1', '648.bi1', '648.bi3', '648.bi5', '648.bi6', '648.bj1', '648.bj2', '648.bm1', '648.bm2', '648.bm4', '648.bm6', '648.bm7', '648.bm8', '648.bm11', '648.bm13', '648.bn2', '648.bo1', '648.bo2', '648.bp3', '648.bp4', '648.bp5', '648.bq3', '648.bq5', '648.bq6', '648.br2', '648.bt1', '648.bu1', '648.bw1', '648.bw3', '648.by1', '648.by3', '648.cd2', '648.cd3', '648.cd4', '648.ce1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2315, -1, 2785, -1], 'generators': [3228220166065152596642611544, 2516538717431153201374234121, 1646776838392686240813757890, 2094763166518129150911744344], 'label': '17496.ec.216.be2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.be2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301979
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.be3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['72.b1', '72.c1', '72.d1', '108.bd3'], 'contains': ['648.bh2', '648.bi2', '648.bi3', '648.bi5', '648.bi7', '648.bj2', '648.bm1', '648.bm3', '648.bm4', '648.bm8', '648.bm9', '648.bm12', '648.bm14', '648.bn1', '648.bn2', '648.bo1', '648.bo3', '648.bp1', '648.bp2', '648.bp3', '648.bp6', '648.bq1', '648.bq2', '648.bq4', '648.br2', '648.bt1', '648.bu1', '648.bw1', '648.bw3', '648.by2', '648.by4', '648.cd2', '648.cd3', '648.cd4', '648.ce1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [2533, -1, 2748, -1], 'generators': [3228220166065152596642611544, 840788568360280067521870080, 513163763439777541426406400, 2094763166518129150911744344], 'label': '17496.ec.216.be3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.be3', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301980
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['3.a1'], 'contains': ['54.e1', '243.b1', '243.c1'], 'core': '17496.a1', 'coset_action_label': '27T951', 'count': 81, 'diagramx': [9975, -1, 9937, -1], 'generators': [3228220166063390033219386121, 2420451374262606871357585146, 3228220166062885089288269321, 1646776838392686240813847332, 112435075062505589522013479, 47882431127126422787571329, 2094763166516995115581614793], 'label': '17496.ec.27.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.c1', 'old_label': '27.c1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1', 'subgroup_fusion': None, 'weyl_group': '648.730'}
    • id: 157301981
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '72.d1', '108.be1'], 'contains': ['648.bg1', '648.bg2', '648.bi4', '648.bi5', '648.bm1', '648.bm4', '648.bm5', '648.bm8', '648.bm10', '648.bp3', '648.bp7', '648.bq1', '648.bq3', '648.bq5', '648.bs1', '648.bt1', '648.bw1', '648.bw2', '648.bw3', '648.bx3', '648.by2', '648.by3', '648.cd1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1933, -1, 2601, -1], 'generators': [513163763439777541426406400, 3228220166065479540661533732, 2094763166517755155164295680, 1258350440042503593257779544], 'label': '17496.ec.216.bf1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bf1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301982
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bf2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['72.c1', '72.d1', '108.be2'], 'contains': ['648.bg2', '648.bi4', '648.bi7', '648.bm7', '648.bm11', '648.bp2', '648.bq4', '648.bq5', '648.br2', '648.bs1', '648.bz1', '648.ca2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [1494, -1, 2270, -1], 'generators': [324885, 3228220166064355282675774762, 174793, 2094763166518129150911744344], 'label': '17496.ec.216.bf2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bf2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301983
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bf3', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '72.d1', '108.be3'], 'contains': ['648.bg1', '648.bg2', '648.bi1', '648.bi7', '648.bm2', '648.bm6', '648.bm12', '648.bm13', '648.bm14', '648.bp4', '648.bp6', '648.bq2', '648.bq4', '648.bq6', '648.bs1', '648.bt1', '648.bw1', '648.bw2', '648.bw3', '648.bx1', '648.bx2', '648.by1', '648.by4', '648.cd1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1682, -1, 2564, -1], 'generators': [1258350440042503593257566762, 3228220166065479540661533732, 2094763166517755155164295680, 1258350440042503593257779544], 'label': '17496.ec.216.bf3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bf3', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf3', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301984
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bf4', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['72.c1', '72.d1', '108.be4'], 'contains': ['648.bg1', '648.bi1', '648.bi5', '648.bm3', '648.bm9', '648.bp1', '648.bp5', '648.bq1', '648.bq2', '648.bq3', '648.bq6', '648.br1', '648.br2', '648.bs1', '648.bz1', '648.ca1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [2183, -1, 2417, -1], 'generators': [2900600827630409708907655680, 2900600827630409708907704085, 3228220166065479540661533732, 2094763166517755155164295680], 'label': '17496.ec.216.bf4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bf4', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf4', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301985
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['72.b1', '72.d1', '108.bf1'], 'contains': ['648.bi1', '648.bi4', '648.bi5', '648.bi7', '648.bn1', '648.bn2', '648.bo1', '648.bo2', '648.bo3', '648.bv1', '648.by1', '648.by2', '648.by3', '648.by4', '648.cf1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [3480, -1, 2086, -1], 'generators': [3228220166062885089288269321, 324885, 2900600827630409708907704085, 2094763166516995115581614793], 'label': '17496.ec.216.bg1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bg1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bg1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301986
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['72.c1', '72.d1', '108.bg1'], 'contains': ['648.bi6', '648.bj1', '648.bo1', '648.bo2', '648.bq2', '648.bq5', '648.bu1', '648.bw3', '648.bx1', '648.bx3', '648.by2', '648.by4', '648.bz1', '648.ca1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [971, -1, 2049, -1], 'generators': [3228220166065152596642611544, 1646776838392686240813757890, 2094763166518129150911744344, 3228220166063390033219447490], 'label': '17496.ec.216.bh1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bh1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301987
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bh2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['72.c1', '72.d1', '108.bg2'], 'contains': ['648.bi2', '648.bi3', '648.bj2', '648.bo1', '648.bo2', '648.bo3', '648.bq1', '648.bq3', '648.bq4', '648.bq6', '648.bu1', '648.bw1', '648.bw2', '648.bx2', '648.bx3', '648.by1', '648.by3', '648.by4', '648.bz1', '648.ca1', '648.ca2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [947, -1, 2159, -1], 'generators': [2094763166518465308968928000, 3228220166065152596642611544, 513163763439777541426406400, 2094763166518129150911744344], 'label': '17496.ec.216.bh2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1', 'old_label': '216.bh2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 157301988
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['72.d1', '108.bh1'], 'contains': ['648.bt1', '648.bv1', '648.ca1', '648.ca2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4706, -1, 1572, -1], 'generators': [3228220166062885089288269321, 324885, 174793, 2094763166516995115581614793], 'label': '17496.ec.216.bi1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '216.bi1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bi1', 'subgroup_fusion': None, 'weyl_group': '8.4'}
    • id: 157301989
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '216.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['72.b1', '108.bi1'], 'contains': ['648.cc1', '648.cc2', '648.cd2', '648.cd3', '648.cd4', '648.cf1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6219, -1, 3484, -1], 'generators': [3228220166062885089288269321, 2094763166516995115581614793, 1258350440042503593257779544, 840788568360280067521768393], 'label': '17496.ec.216.bj1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1', 'old_label': '216.bj1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bj1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
    • id: 157301990
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.b1', '81.a1'], 'contains': ['486.a1', '2187.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9967, -1, 9893, -1], 'generators': [3228220166063390033219633685, 47882431127126422787571329, 33014302651624106797526800, 112435075063470840937936679, 2094763166518465308969156132], 'label': '17496.ec.243.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '243.a1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 157301991
      {'ambient': '17496.ec', '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': '17496.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1'], 'contains': ['72.f1', '108.a1', '108.b1', '108.d1', '108.u1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [154, -1, 716, -1], 'generators': [1884795613975332, 112435075063470840938075215, 4615839911531101360447237799, 3228220166063390033219633685, 174793, 2094763166518465308969156132], 'label': '17496.ec.36.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.a1', 'old_label': '36.a1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '486.167'}
    • id: 157301992
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '243.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['27.a1', '27.c1'], 'contains': ['486.b1', '2187.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 729, 'diagramx': [9872, -1, 9982, -1], 'generators': [3228220166063390033219386121, 2420451374262606871357585146, 1646776838392686240813847332, 47882431127126422787571329, 1241521906133306944273921919], 'label': '17496.ec.243.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.b1', 'old_label': '243.b1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.b1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 157301993
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '243.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.b1', '27.c1'], 'contains': ['486.c1', '2187.a1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 243, 'diagramx': [9993, -1, 9937, -1], 'generators': [3228220166062885089288269321, 2499866465850354518654555215, 47882431127126422787571329, 2094763166516995115581614793, 33014302651624106797526800], 'label': '17496.ec.243.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '243.c1', 'old_label': '243.c1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.c1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 157301994
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.b1', '108.d1'], 'contains': ['648.t1', '972.a1', '972.e1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [91, -1, 611, -1], 'generators': [2111439868000061395631025434, 2849517334059285, 4615839911531101360447237799, 3228220166063390033219633685], 'label': '17496.ec.324.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.a1', 'old_label': '324.a1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 157301995
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.c1', '108.d1'], 'contains': ['648.z1', '972.a1', '972.h1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [49, -1, 490, -1], 'generators': [112435075063470840937901175, 3228220166065152596642611544, 4615839911531101360447237799, 2094763166518465308969156132], 'label': '17496.ec.324.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.b1', 'old_label': '324.b1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 157301996
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1', '162.a1'], 'contains': ['648.be1', '972.a1', '972.i1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [4841, -1, 550, -1], 'generators': [112435075063470840937901175, 4615839911531101360447237799, 3228220166063390033219633685, 2094763166518465308969156132], 'label': '17496.ec.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.c1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 157301997
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['108.e1', '108.e2', '108.e3', '108.f2', '108.i1', '108.k2', '108.l1', '108.l2', '108.n1', '108.r1'], 'contains': ['648.a1', '972.b1', '972.d1', '972.f1', '972.j1', '972.l1', '972.l2', '972.t1', '972.z1', '972.z2', '972.z3'], 'core': '17496.a1', 'coset_action_label': None, 'count': 11664, 'diagramx': [5680, -1, 5304, -1], 'generators': [112435075062505589522013479, 3228220166064769884902215680, 2094763166519844632915313090, 1134035330304344], 'label': '17496.ec.324.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d1', 'old_label': '324.d1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157301998
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.d2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['108.e1', '108.e3', '108.f2', '108.i1', '108.k1', '108.l2', '108.n2', '108.r1'], 'contains': ['648.a2', '972.b1', '972.d1', '972.f1', '972.j2', '972.l1', '972.t2', '972.z1', '972.z2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [5362, -1, 4999, -1], 'generators': [112435075062505589522013479, 3228220166064769884902215680, 2094763166519844632915313090, 3228220166063390033219447490], 'label': '17496.ec.324.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.d2', 'old_label': '324.d2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d2', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157301999
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['108.g1', '108.h1', '108.i1', '108.p1', '108.r1'], 'contains': ['648.b1', '972.b1', '972.e1', '972.f1', '972.j1', '972.j2', '972.t1', '972.t2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [4593, -1, 4340, -1], 'generators': [2267507354388480, 1646776838392686240813847332, 1258350440042503593257610690, 112435075062505589522013479], 'label': '17496.ec.324.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.e1', 'old_label': '324.e1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302000
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['108.f2', '108.j1', '108.j2', '108.j3', '108.m1', '108.m2', '108.r1'], 'contains': ['648.c1', '972.b1', '972.f1', '972.h1', '972.l1', '972.l2', '972.z1', '972.z2', '972.z3'], 'core': '17496.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [4606, -1, 5405, -1], 'generators': [112435075062505589522013479, 2094763166519844632915313090, 174793, 3228220166064019124618363593], 'label': '17496.ec.324.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.f1', 'old_label': '324.f1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302001
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['108.e1', '108.e2', '108.e3', '108.g1', '108.k1', '108.k2', '108.m1', '108.m2', '108.t1'], 'contains': ['648.d1', '972.b1', '972.f1', '972.g1', '972.k1', '972.k2', '972.k3', '972.ba1', '972.ba2', '972.ba3', '972.ba4'], 'core': '17496.a1', 'coset_action_label': None, 'count': 11664, 'diagramx': [7061, -1, 6369, -1], 'generators': [112435075062505589522013479, 3228220166063390033219633685, 1646776838391306389131066121, 2094763166518465308969235544], 'label': '17496.ec.324.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.g1', 'old_label': '324.g1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302002
      {'ambient': '17496.ec', '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': '17496.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.b1'], 'contains': ['72.j1', '108.c1', '108.d1', '108.w1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [136, -1, 583, -1], 'generators': [1884795613975332, 4615839911531101360447237799, 112435075062505589522013479, 3228220166063390033219633685, 2267507354189321, 2094763166518465308969156132], 'label': '17496.ec.36.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1', 'old_label': '36.b1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '486.167'}
    • id: 157302003
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['108.e1', '108.e2', '108.e3', '108.h1', '108.j2', '108.j3', '108.k1', '108.k2', '108.l1', '108.l2', '108.n1', '108.s1'], 'contains': ['648.e1', '972.b1', '972.f1', '972.f2', '972.m1', '972.m2', '972.m3', '972.bb1', '972.bb2', '972.bb3'], 'core': '17496.a1', 'coset_action_label': None, 'count': 11664, 'diagramx': [6062, -1, 5760, -1], 'generators': [1646776838391306389131216932, 2094763166517755155164096521, 112435075062505589522013479, 3228220166063390033219633685], 'label': '17496.ec.324.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.h1', 'old_label': '324.h1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302004
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.h2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['108.e1', '108.e2', '108.h1', '108.j1', '108.j3', '108.k2', '108.l2', '108.n2', '108.s1'], 'contains': ['648.e2', '972.b1', '972.f1', '972.f2', '972.m1', '972.m2', '972.m4', '972.bb1', '972.bb2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [5708, -1, 5507, -1], 'generators': [1646776838391306389131216932, 112435075062505589522013479, 3228220166063390033219633685, 1884795613747200], 'label': '17496.ec.324.h2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.h2', 'old_label': '324.h2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h2', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302005
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['108.e1', '108.h1', '108.j1', '108.j3', '108.k1', '108.k2', '108.l1', '108.n1', '108.t1'], 'contains': ['648.f1', '972.b1', '972.f1', '972.f2', '972.k1', '972.k2', '972.p1', '972.ba1', '972.ba2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 5832, 'diagramx': [5614, -1, 5456, -1], 'generators': [1646776838391306389131216932, 2594451373438485, 112435075062505589522013479, 3228220166063390033219633685], 'label': '17496.ec.324.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i1', 'old_label': '324.i1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302006
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.i2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 36, 'contained_in': ['108.e2', '108.e3', '108.h1', '108.j2', '108.j3', '108.k1', '108.k2', '108.l2', '108.n1', '108.n2', '108.t1'], 'contains': ['648.f2', '972.b1', '972.f1', '972.f2', '972.k1', '972.k2', '972.k3', '972.p2', '972.ba1', '972.ba3', '972.ba4'], 'core': '17496.a1', 'coset_action_label': None, 'count': 11664, 'diagramx': [6042, -1, 5811, -1], 'generators': [760039582753993, 112435075062505589522013479, 1646776838390801445199872000, 3228220166063390033219633685], 'label': '17496.ec.324.i2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.i2', 'old_label': '324.i2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i2', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302007
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['108.f1', '108.l1', '108.n2', '108.o1', '108.r1'], 'contains': ['648.g1', '972.c1', '972.d1', '972.f2', '972.j2', '972.l2'], 'core': '17496.a1', 'coset_action_label': None, 'count': 972, 'diagramx': [3166, -1, 4036, -1], 'generators': [112435075062505589522013479, 3228220166064769884902215680, 3228220166064355282675956480, 2094763166518465308969156132], 'label': '17496.ec.324.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.j1', 'old_label': '324.j1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302008
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.j2', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['108.f1', '108.l2', '108.n1', '108.o1', '108.r1'], 'contains': ['648.g2', '972.c1', '972.d1', '972.f2', '972.j1', '972.l1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [3179, -1, 4086, -1], 'generators': [112435075062505589522013479, 3228220166064769884902215680, 513163763438812819706744085, 2094763166518465308969156132], 'label': '17496.ec.324.j2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.j2', 'old_label': '324.j2', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j2', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302009
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['108.f2', '108.i1', '108.k1', '108.k2', '108.n1', '108.n2', '108.u1'], 'contains': ['648.h1', '972.b1', '972.d1', '972.n1', '972.r1', '972.v1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 2916, 'diagramx': [5239, -1, 4391, -1], 'generators': [1646776838392686240813847332, 112435075062505589522013479, 3228220166063390033219633685, 2094763166516995115581614793], 'label': '17496.ec.324.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.k1', 'old_label': '324.k1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302010
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['108.l1', '108.l2', '108.m2', '108.p1', '108.s1'], 'contains': ['648.i1', '972.c1', '972.f1', '972.m1', '972.m2', '972.m3', '972.m4'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [4017, -1, 4492, -1], 'generators': [2094763166518129150911761685, 324885, 112435075062505589522013479, 3228220166063390033219633685], 'label': '17496.ec.324.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.l1', 'old_label': '324.l1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.l1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302011
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.f1', '108.m1', '108.m2', '108.u1'], 'contains': ['648.j1', '972.c1', '972.g1', '972.h1', '972.n1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [3332, -1, 3934, -1], 'generators': [3228220166063645128870909890, 112435075062505589522013479, 174793, 2094763166518465308969156132], 'label': '17496.ec.324.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.m1', 'old_label': '324.m1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.m1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
    • id: 157302012
      {'ambient': '17496.ec', 'aut_centralizer_order': None, 'aut_label': '324.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '17496.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['108.g1', '108.k1', '108.k2', '108.m1', '108.v1'], 'contains': ['648.k1', '972.b1', '972.g1', '972.o1', '972.q1', '972.be1'], 'core': '17496.a1', 'coset_action_label': None, 'count': 1944, 'diagramx': [5736, -1, 4898, -1], 'generators': [112435075062505589522013479, 3228220166063390033219633685, 174793, 1646776838392686240813757890], 'label': '17496.ec.324.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.n1', 'old_label': '324.n1', 'projective_image': '17496.ec', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.n1', 'subgroup_fusion': None, 'weyl_group': '54.14'}