Formats: - HTML - YAML - JSON - 2026-07-21T03:35:43.379677
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '36.14', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [6, 18, 36, 6], 'aut_gens': [[159556232672278924018461017628285849450812, 74459448316068278439886730038647718997636], [180225788114618376402283632081431041357561, 212138601881649722740007212741072026243575], [307870812028938382896471657922161373369531, 319114375384641712484599339874031322407745], [307870812046621488108253354102631787074491, 361357892640212461862949779800639793103959], [31911192496702211735632261285783142986172, 84490318440079029109925317703482938206645]], 'aut_group': None, 'aut_hash': 800317199862745997, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 76527504, 'aut_permdeg': 891, 'aut_perms': 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'aut_phi_ratio': 324.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 243, 2, 1], [2, 729, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 2], [3, 2, 4, 1], [3, 4, 1, 1], [3, 4, 2, 5], [3, 4, 4, 1], [3, 18, 6, 2], [3, 36, 1, 1], [3, 36, 2, 2], [3, 36, 4, 1], [3, 36, 6, 2], [3, 36, 54, 1], [3, 81, 1, 2], [3, 108, 3, 2], [3, 108, 36, 2], [3, 162, 2, 1], [3, 162, 12, 3], [3, 324, 6, 3], [3, 324, 12, 5], [3, 324, 18, 2], [6, 243, 4, 1], [6, 486, 2, 1], [6, 486, 4, 1], [6, 729, 2, 1], [6, 1458, 1, 1], [6, 1458, 2, 1], [6, 1458, 6, 2], [6, 2187, 2, 2], [6, 4374, 2, 1], [6, 4374, 12, 3], [6, 6561, 1, 2], [9, 54, 6, 1], [9, 108, 3, 1], [9, 108, 6, 2], [9, 243, 2, 1], [9, 324, 6, 4], [9, 486, 1, 1], [9, 486, 2, 5], [9, 729, 2, 2], [9, 972, 1, 2], [9, 972, 2, 3], [9, 972, 6, 7], [9, 972, 12, 3], [9, 1458, 1, 2], [9, 1458, 2, 2], [9, 2916, 2, 2], [18, 2187, 2, 1], [18, 4374, 1, 1], [18, 4374, 2, 2], [18, 4374, 6, 1], [18, 6561, 2, 2], [18, 6561, 4, 3], [18, 13122, 1, 2], [18, 13122, 2, 5]], 'aut_supersolvable': False, 'aut_tex': 'C_3^5.C_3^5.C_6.C_6^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 3, 'autcent_group': '9.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 9, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': None, 'autcentquo_hash': 6176671763908363530, 'autcentquo_nilpotent': False, 'autcentquo_order': 8503056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^5.C_3^5.C_6^2.C_2^2', 'cc_stats': [[1, 1, 1], [2, 243, 2], [2, 729, 1], [3, 1, 2], [3, 2, 9], [3, 4, 15], [3, 18, 12], [3, 36, 75], [3, 81, 2], [3, 108, 78], [3, 162, 38], [3, 324, 114], [6, 243, 4], [6, 486, 6], [6, 729, 2], [6, 1458, 15], [6, 2187, 4], [6, 4374, 38], [6, 6561, 2], [9, 54, 6], [9, 108, 15], [9, 243, 2], [9, 324, 24], [9, 486, 11], [9, 729, 4], [9, 972, 86], [9, 1458, 6], [9, 2916, 4], [18, 2187, 2], [18, 4374, 11], [18, 6561, 16], [18, 13122, 12]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 226, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 243, 1, 2], [2, 729, 1, 1], [3, 1, 2, 1], [3, 2, 1, 3], [3, 2, 2, 3], [3, 4, 1, 3], [3, 4, 2, 6], [3, 18, 2, 6], [3, 36, 1, 3], [3, 36, 2, 36], [3, 81, 2, 1], [3, 108, 2, 39], [3, 162, 1, 2], [3, 162, 2, 18], [3, 324, 1, 6], [3, 324, 2, 54], [6, 243, 2, 2], [6, 486, 1, 2], [6, 486, 2, 2], [6, 729, 2, 1], [6, 1458, 1, 1], [6, 1458, 2, 7], [6, 2187, 2, 2], [6, 4374, 1, 2], [6, 4374, 2, 18], [6, 6561, 2, 1], [9, 54, 2, 3], [9, 108, 1, 3], [9, 108, 2, 6], [9, 243, 2, 1], [9, 324, 2, 12], [9, 486, 1, 3], [9, 486, 2, 4], [9, 729, 2, 2], [9, 972, 1, 4], [9, 972, 2, 38], [9, 972, 6, 1], [9, 1458, 2, 3], [9, 2916, 2, 2], [18, 2187, 2, 1], [18, 4374, 1, 1], [18, 4374, 2, 5], [18, 6561, 2, 8], [18, 13122, 1, 2], [18, 13122, 2, 5]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 18, 'exponents_of_order': [11, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 162], [36, 0, 36], [108, 0, 6]], 'familial': False, 'frattini_label': '729.504', 'frattini_quotient': '972.886', 'hash': 3977320648544937282, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [18, 6], 'inner_gens': [[159556232672278924018461017628285849450812, 329748715175240996574009730176253699544131], [307870811955056145406024420522603476319436, 74459448316068278439886730038647718997636]], 'inner_hash': 5674166624757429411, 'inner_nilpotent': False, 'inner_order': 236196, 'inner_split': None, 'inner_tex': 'C_3^5.C_3^5.C_2^2', 'inner_used': [1, 2], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 36], [2, 54], [4, 45], [12, 189], [18, 96], [27, 8], [36, 141], [54, 14], [108, 36]], 'label': '708588.ir', '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': True, 'name': 'C3^7.C3wrC2^2', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 115, 'number_characteristic_subgroups': 37, 'number_conjugacy_classes': 619, 'number_divisions': 327, 'number_normal_subgroups': 111, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 708588, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 1215], [3, 54674], [6, 215298], [9, 122472], [18, 314928]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6, 3, 6, 3], 'outer_gen_pows': [526261673867387065200240040673360640, 17683942790150574557177061504243, 526279357391374544604860502761552880, 9147456921273669403100862566548], 'outer_gens': [[297835901471690919611424602063587355766235, 351323762987056361313309245298444199600052], [170184868328019816370378298966801633095435, 202098242126261951765840839451528304254131], [297832896961689025381587228679196825953322, 212136157311294145300618171861239971229506], [297835629944637300495027735804064001067599, 319114901646310934574473079368752262674085]], 'outer_group': '324.165', 'outer_hash': 165, 'outer_nilpotent': False, 'outer_order': 324, 'outer_permdeg': 36, 'outer_perms': [181601997146546872426819794568850498025277, 75888255056576118362899279068617088993073, 257146959513973420353980184877121433463169, 119472069513358475022492255618482827692046], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^2\\times S_3^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 22], [4, 27], [8, 21], [12, 3], [18, 4], [24, 93], [36, 55], [54, 10], [72, 66], [108, 8], [216, 13], [648, 1]], 'representations': {'PC': {'code': '943257611703485849748029354472198247655696435812736220007775074678866305754879324723810009204338010911121433855990114972657065849578185705111793634369641387227888073314101324815627799031737352132413598243223111635427385908669473448939344555742703628318575515597037523325437845325841950366834834777455307775', 'gens': [1, 3, 5, 6, 8, 10, 11, 12, 13], 'pres': [13, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 26, 179480, 3938352, 106, 34015491, 303592, 947742, 30539344, 20966417, 1898160, 2436178, 3925589, 15041070, 6303991, 3054446, 114717, 304, 9860, 36897127, 21885572, 10052673, 4077262, 1746635, 439056, 410, 682352, 113758, 18954009, 7034062, 7651835, 129918, 402541, 273854, 30520, 58424662, 44455577, 8000028, 351400, 2468528, 532893, 94052, 69700187, 24842400, 3639205, 1391427, 796144, 50646, 36960312]}, 'Perm': {'d': 36, 'gens': [74459448316068278439886730038647718997636, 159556232672278924018461017628285849450812]}}, 'schur_multiplier': [6], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [6, 6], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 27, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^7.C_3\\wr C_2^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    Showing the first 100 of 619 matching records in this table.
    • id: 166850742
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 226, 'group_order': 708588, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 166850853
      {'aut_label': '2A', 'centralizer': None, 'counter': 2, 'group_counter': 226, 'group_order': 708588, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 63824548696351395665216576827559881425845, 'size': 243}
    • id: 166850964
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    • id: 166851346
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 86, 'group_counter': 226, 'group_order': 708588, 'label': '3AT1', 'order': 3, 'powers': [87, 1], 'representative': 271463567735518196447053698524817844, 'size': 36}
    • id: 166851347
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 87, 'group_counter': 226, 'group_order': 708588, 'label': '3AT-1', 'order': 3, 'powers': [86, 1], 'representative': 526481456485527428113651202689691764, 'size': 36}
    • id: 166851348
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 88, 'group_counter': 226, 'group_order': 708588, 'label': '3AU1', 'order': 3, 'powers': [89, 1], 'representative': 271573457787209147282588439499281844, 'size': 36}
    • id: 166851349
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 89, 'group_counter': 226, 'group_order': 708588, 'label': '3AU-1', 'order': 3, 'powers': [88, 1], 'representative': 526371565596231134937866340599349123, 'size': 36}
    • id: 166851351
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 90, 'group_counter': 226, 'group_order': 708588, 'label': '3AV1', 'order': 3, 'powers': [91, 1], 'representative': 271573457787209147282965143122578083, 'size': 36}
    • id: 166851352
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 91, 'group_counter': 226, 'group_order': 708588, 'label': '3AV-1', 'order': 3, 'powers': [90, 1], 'representative': 526371565596231134938577889812123668, 'size': 36}
    • id: 166851353
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 92, 'group_counter': 226, 'group_order': 708588, 'label': '3AW1', 'order': 3, 'powers': [93, 1], 'representative': 271573458206011818452901845641848484, 'size': 36}
    • id: 166851354
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 93, 'group_counter': 226, 'group_order': 708588, 'label': '3AW-1', 'order': 3, 'powers': [92, 1], 'representative': 526371566015033806107803055572661124, 'size': 36}
    • id: 166851355
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 94, 'group_counter': 226, 'group_order': 708588, 'label': '3AX1', 'order': 3, 'powers': [95, 1], 'representative': 3259463762317318632250156515507937347, 'size': 36}
    • id: 166851356
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 95, 'group_counter': 226, 'group_order': 708588, 'label': '3AX-1', 'order': 3, 'powers': [94, 1], 'representative': 6518899440950951706802167959750955124, 'size': 36}
    • id: 166851357
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 96, 'group_counter': 226, 'group_order': 708588, 'label': '3AY1', 'order': 3, 'powers': [97, 1], 'representative': 3259463762317345605956366270288196627, 'size': 36}
    • id: 166851358
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 97, 'group_counter': 226, 'group_order': 708588, 'label': '3AY-1', 'order': 3, 'powers': [96, 1], 'representative': 6518899440951003413146902637508295844, 'size': 36}
    • id: 166851359
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 98, 'group_counter': 226, 'group_order': 708588, 'label': '3AZ1', 'order': 3, 'powers': [99, 1], 'representative': 3259463762705098883333431246059207748, 'size': 36}
    • id: 166851360
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 99, 'group_counter': 226, 'group_order': 708588, 'label': '3AZ-1', 'order': 3, 'powers': [98, 1], 'representative': 6518899440563171455718893229199684723, 'size': 36}
    • id: 166850744
      {'aut_label': '3AF1', 'centralizer': None, 'counter': 100, 'group_counter': 226, 'group_order': 708588, 'label': '3BA1', 'order': 3, 'powers': [101, 1], 'representative': 3259463762705125857039641000839467028, 'size': 36}
  • group 708588.ir does not appear in gps_qchar
  • group 708588.ir does not appear in gps_char
  • gps_subgroup_search • Show schema
    Showing the first 100 of 176 matching records in this table.
    • id: 244264719
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 708588, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '708588.ir.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'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '708588.ir', 'subgroup_hash': 3977320648544937282, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^7.C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 244264807
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 354294, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.2.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2398769240071516874, 'subgroup_order': 354294, 'subgroup_tex': 'C_3^6.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264818
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 354294, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8850084279543578570, 'subgroup_order': 354294, 'subgroup_tex': 'C_3^6.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264829
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 236196, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.3.A', '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': '236196.jt', 'subgroup_hash': 377171881584926644, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 244264840
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 236196, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.3.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.b1', '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': '236196.lh', 'subgroup_hash': 8198807337538431408, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 244264851
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.3.C', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.c1', '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': '236196.lj', 'subgroup_hash': 8395398433800102311, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 244264862
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.3.D', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.iy', 'subgroup_hash': 4104829636642293084, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^7.(C_3\\times S_3^2)', 'supersolvable': True, 'sylow': 0}
    • id: 244264873
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.3.E', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.jd', 'subgroup_hash': 1539677475667236896, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^7.(C_3\\times S_3^2)', 'supersolvable': True, 'sylow': 0}
    • id: 244264884
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 177147, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '708588.ir.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['F', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3709646357928050309, 'subgroup_order': 177147, 'subgroup_tex': 'C_3^7.C_3^4', 'supersolvable': True, 'sylow': 3}
    • id: 244264720
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5800995218981330681, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264731
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5800995218981330681, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264742
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4514826845252250347, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264753
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 859727553309180838, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264764
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 118098, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4631506730004189135, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264775
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 118098, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.f1', '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': 4631506730004189135, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^5.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264786
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 118098, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.g1', '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': 3518229174562669243, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264797
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.h1', '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': 2392801265462438997, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264805
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7142729956278922192, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264806
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5113680101513133645, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^5.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264808
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5113680101513133645, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264809
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 131685665356923625, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264810
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1705278542805115316, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264811
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 859727553309180838, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264812
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 245919802997574010, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264813
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3222173999379720031, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264814
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 774317831150861714, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264815
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6667803214483575295, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264816
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.6.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2392801265462438997, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^5.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264817
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 78732, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.9.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6539010332495766906, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.\\He_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264819
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.9.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.ja', 'subgroup_hash': 4644933730929525816, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 244264820
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.9.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.ji', 'subgroup_hash': 430476649419916604, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 244264821
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.9.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.ho', 'subgroup_hash': 985680530100474780, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 244264822
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.9.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8906847388816749675, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 244264823
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.9.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': None, 'subgroup_hash': 8906847388816749675, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^3.C_6.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264824
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.9.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '78732.hw', 'subgroup_hash': 5217715847800764535, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 244264825
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.9.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '78732.kq', 'subgroup_hash': 5255198837148696317, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.(C_3\\times S_3^2)', 'supersolvable': True, 'sylow': 0}
    • id: 244264826
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.9.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': None, 'subgroup_hash': 6713378673419489337, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 244264827
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6127100435953899114, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264828
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 59049, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6127100435953899114, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264830
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 59049, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6127100435953899114, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264831
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 59049, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.d1', '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': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 56042109095087524, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264832
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.e1', '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': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4992456160288247897, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264833
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6445998730009855764, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264834
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6445998730009855764, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264835
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6445998730009855764, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264836
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5979481490271948439, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264837
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5979481490271948439, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264838
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1244878079420439474, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264839
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1244878079420439474, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264841
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.M', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3853812658439650071, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264842
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.N', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 6127100435953899114, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^7.C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 244264843
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.O', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 7652891007608811243, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264844
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 7652891007608811243, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264845
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 7652891007608811243, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264846
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.R', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 8808814257329811720, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264847
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.S', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 8808814257329811720, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264848
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.T', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 6088201557326944701, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264849
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.U', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 6088201557326944701, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264850
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.V', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 1052809912819436, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264852
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.W', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 4992456160288247897, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264853
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.X', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 4992456160288247897, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264854
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.12.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': None, 'subgroup_hash': 4992456160288247897, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 244264855
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9082106629485287071, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264856
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4440142176676465768, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264857
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7877293562513805723, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264858
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7877293562513805723, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264859
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 39366, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4549194247579291947, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264860
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1617664516712860841, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264861
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 39366, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1617664516712860841, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264863
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 39366, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1617664516712860841, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264864
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1059603805462793365, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^7.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264865
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 412626310032813919, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^4.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264866
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4782344203385586137, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264867
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8971104525389290841, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264868
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8971104525389290841, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264869
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3520786820377851561, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264870
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5626547268530934097, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264871
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5626547268530934097, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264872
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3520786820377851561, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264874
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8682008270200902513, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264875
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 8682008270200902513, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264876
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 7999269442015727279, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264877
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 7999269442015727279, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264878
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 7999269442015727279, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264879
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 7999269442015727279, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264880
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 7999269442015727279, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264881
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 7468533263957748224, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264882
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 7468533263957748224, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264883
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 4144341226551984197, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264885
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 7468533263957748224, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264886
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 7468533263957748224, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264887
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 4144341226551984197, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264888
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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': None, 'subgroup_hash': 4144341226551984197, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264889
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bf1', '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': None, 'subgroup_hash': 4144341226551984197, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264890
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bg1', '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': None, 'subgroup_hash': 5955212944316845953, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264891
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bh1', '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': None, 'subgroup_hash': 5955212944316845953, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264892
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bi1', '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': None, 'subgroup_hash': 4440142176676465768, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264893
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bj1', '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': None, 'subgroup_hash': 5450558530638744517, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^7.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 244264894
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 243, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bk1', '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': None, 'subgroup_hash': 105992602274268618, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 244264721
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '708588.ir', 'ambient_counter': 226, 'ambient_order': 708588, 'ambient_tex': 'C_3^7.C_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 243, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '708588.ir.18.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bl1', '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': None, 'subgroup_hash': 726261812937908609, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^4.C_3^3.C_3.C_6', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 176 matching records in this table.
    • id: 244264719
      {'ambient': '708588.ir', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [104, 1310, 38, 91], 'generators': [6790345324355951192832502384381801104, 526270820517725416616431696011344784, 51706588024878582378240, 10628652136785279759096401461690034887203, 418802671169936714973312003, 119047606003398925678629914726400, 159556232672278924018461017628285849450812, 17683942790150574557177061504243, 4865804109758637364, 138276680670356016853249968186779369783043, 376703623296244, 74459448316068278439886730038647718997636, 10066262937301299313346728917], 'label': '708588.ir.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': None, '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': None}
    • id: 244264720
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '6.A', 'coset_action_label': None, 'count': 2, 'diagramx': [1487, 4582, 1380, 1958], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 233718827641170969604125301755226769444642, 127579446523390330757272614416164, 17683942790150574557177061504243, 376703623296244, 4865804109758637364, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.A', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264721
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2916.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1780, -1, 5253, -1], 'generators': [138276680780252778828862683476067478087203, 51706588024878582378240, 10628652128248793890219496307613835949508, 4866180800927892003, 418802671169936714973312003, 127579446523390330757272614416164, 526261674286189736370176755646672643, 159556232672278924018461017628285849450812, 275960179627539264660514694425175591591280, 17683942790150574557177061504243], 'label': '708588.ir.18.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.BL', 'old_label': '18.bl1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BL', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264722
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '324.A', 'coset_action_label': None, 'count': 6, 'diagramx': [9927, -1, 8896, -1], 'generators': [51706588024878582378240, 17683942790150574557177061504243, 526261674286189736370176755646672643, 119047606003398925678629914726400, 376703623296244, 10628652128248793890219496307613835949508, 418802671169936714973312003, 4865804109758637364, 307870811955056145406024420522603476319436, 10066262937301299313346728917], 'label': '708588.ir.18.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '18.bm1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BM', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264723
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3767, -1, 6141, -1], 'generators': [51706588024878582378240, 307867297693797924513119152216739395431119, 3785798708645587992854115866660539680, 17683942790150574557177061504243, 526261674286189736370176755646672643, 376703623296244, 10628652128248793890219496307613835949508, 418802671169936714973312003, 4865804109758637364, 275960179718500734264803501521575448197268], 'label': '708588.ir.18.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '18.bn1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BN', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264724
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.B', 'coset_action_label': None, 'count': 6, 'diagramx': [3932, -1, 6216, -1], 'generators': [51706588024878582378240, 17683942790150574557177061504243, 138276680780252778828862683476067478087203, 526261674286189736370176755646672643, 376703623296244, 138273964847675931875301272455087819690803, 10628652128248793890219496307613835949508, 418802671169936714973312003, 4865804109758637364, 170184613630012996506929348731808078545469], 'label': '708588.ir.18.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '18.bo1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BO', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264725
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '324.A', 'coset_action_label': None, 'count': 6, 'diagramx': [255, -1, 4570, -1], 'generators': [51706588024878582378240, 10628652128248793890219496307613835949508, 138276680670361920525604619375839407597508, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 159556232672278924018461017628285849450812, 17683942790150574557177061504243, 376703623296244, 4865804109758637364], 'label': '708588.ir.18.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '18.bp1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BP', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264726
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.C', 'coset_action_label': None, 'count': 12, 'diagramx': [5345, -1, 6847, -1], 'generators': [6790345331486794053800052574579270563, 51706588024878582378240, 17683942790150574557177061504243, 526261674286189736370176755646672643, 376703623296244, 159556232672278924018461017628285849450812, 10628652128248793890219496307613835949508, 418802671169936714973312003, 4865804109758637364, 275960179718500734264803501521575448197268], 'label': '708588.ir.18.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.P', 'old_label': '18.bq1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BQ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264727
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.A', 'coset_action_label': None, 'count': 6, 'diagramx': [8203, -1, 8125, -1], 'generators': [275962352999916311011770156949156061264640, 51706588024878582378240, 17683942790150574557177061504243, 526261674286189736370176755646672643, 119047606003398925678629914726400, 376703623296244, 10628652128248793890219496307613835949508, 418802671169936714973312003, 42545277067315780556434868261637774056155, 4865804109758637364], 'label': '708588.ir.18.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '18.br1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BR', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264728
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.B', 'coset_action_label': None, 'count': 6, 'diagramx': [8038, -1, 8051, -1], 'generators': [51706588024878582378240, 17683942790150574557177061504243, 138276680780252778828862683476067478087203, 526261674286189736370176755646672643, 376703623296244, 275960179627539264660514694801866760845588, 10628652128248793890219496307613835949508, 418802671169936714973312003, 4865804109758637364, 170184613630012996506929348731808078545469], 'label': '708588.ir.18.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '18.bs1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BS', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264729
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2916.A', 'coset_action_label': None, 'count': 18, 'diagramx': [4849, -1, 6625, -1], 'generators': [26978572013864655018244, 10628652128248793890219496307613835949508, 119047605951692337653751332348160, 418802671169936714973312003, 526261674286189736370176755646672643, 17683942790150574557177061504243, 307870811955056145406024420522603476319436, 376703623296244, 275960179627539264660514694801866760845588, 10066262937301299313346728917], 'label': '708588.ir.18.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.BT', 'old_label': '18.bt1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BT', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264730
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2916.A', 'coset_action_label': None, 'count': 36, 'diagramx': [5842, -1, 7069, -1], 'generators': [26978572013864655018244, 10628652128248793890219496307613835949508, 10066287662762763312093848277, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 17683942790150574557177061504243, 307870811955056145406024420522603476319436, 376703623296244, 275960179627539264660514694801866760845588], 'label': '708588.ir.18.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.BU', 'old_label': '18.bu1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BU', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264731
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '6.B', 'coset_action_label': None, 'count': 2, 'diagramx': [1322, 3466, 1306, 1779], 'generators': [6790345324355951192832502384381801104, 233713649877874817959574233579475816555761, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 119047606003398925678629914726400, 17683942790150574557177061504243, 138276680670356016853249968186779369783043, 4865804109758637364, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264732
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '324.E', 'coset_action_label': None, 'count': 12, 'diagramx': [88, -1, 4496, -1], 'generators': [51706588024878582378240, 10628652128248793890219496307613835949508, 138276680670361920525604619375839407597508, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 159556232672278924018461017628285849450812, 17683942790150574557177061504243, 376703623296244, 138276680670356016853247656929952553164800], 'label': '708588.ir.18.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '18.bv1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BV', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264733
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.G', 'coset_action_label': None, 'count': 6, 'diagramx': [2774, -1, 5697, -1], 'generators': [138276680780252778828862683476067478087203, 51706588024878582378240, 10628652128248793890219496307613835949508, 418802671169936714973312003, 228938464225565425265821550127360, 526261674286189736370176755646672643, 17683942790150574557177061504243, 376703623296244, 275960179627539264660514694801866760845588, 180222528605051213902522335603064762218716], 'label': '708588.ir.18.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '18.bw1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BW', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264734
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '324.E', 'coset_action_label': None, 'count': 12, 'diagramx': [603, -1, 4726, -1], 'generators': [51706588024878582378240, 17683942790150574557177061504243, 526261674286189736370176755646672643, 119047606003398925678629914726400, 376703623296244, 10628652128248793890219496307613835949508, 418802671169936714973312003, 275962352999909631859992616812312630957603, 307870811955056145406024420522603476319436, 10066262937301299313346728917], 'label': '708588.ir.18.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '18.bx1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BX', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264735
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '324.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1946, -1, 5327, -1], 'generators': [51706588024878582378240, 10628652128248793890219496307613835949508, 138276680670361920525604619375839407597508, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 159556232672278924018461017628285849450812, 17683942790150574557177061504243, 376703623296244, 275962352999909631859992616812312630957603], 'label': '708588.ir.18.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '18.by1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BY', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264736
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.I', 'coset_action_label': None, 'count': 12, 'diagramx': [2112, -1, 5401, -1], 'generators': [51706588024878582378240, 17683942790150574557177061504243, 170184613437704673061999269732179767146956, 138276680780252778828862683476067478087203, 526261674286189736370176755646672643, 376703623296244, 275960179627539264660514694801866760845588, 10628652128248793890219496307613835949508, 418802671169936714973312003, 127579446523388019500445797913843], 'label': '708588.ir.18.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '18.bz1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.BZ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264737
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': None, 'contains': None, 'core': '108.D', 'coset_action_label': None, 'count': 24, 'diagramx': [4317, -1, 6388, -1], 'generators': [51706588024878582378240, 3785725445380452538816673803382357638, 17683942790150574557177061504243, 526261674286189736370176755646672643, 376703623296244, 10628652128248793890219496307613835949508, 418802671169936714973312003, 275960179718500734264803501521575448197268, 42539844615803548729303549654294856346812, 271481254615592167279583680466457604], 'label': '708588.ir.18.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.P', 'old_label': '18.ca1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.CA', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264738
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': None, 'contains': None, 'core': '36.E', 'coset_action_label': None, 'count': 12, 'diagramx': [4116, -1, 6297, -1], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 51706588024878582378240, 10628652128248793890219496307613835949508, 170184613437704673061999269732179767146956, 127579446523388019500445797913843, 418802671169936714973312003, 526261674286189736370176755646672643, 17683942790150574557177061504243, 376703623296244], 'label': '708588.ir.18.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '18.cb1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.CB', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264739
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.E', 'coset_action_label': None, 'count': 12, 'diagramx': [4519, -1, 6478, -1], 'generators': [6790345331486794053800052574579270563, 51706588024878582378240, 3785725445380452538816673803382357638, 17683942790150574557177061504243, 526261674286189736370176755646672643, 376703623296244, 159556232672278924018461017628285849450812, 10628652128248793890219496307613835949508, 418802671169936714973312003, 275960179718500734264803501521575448197268], 'label': '708588.ir.18.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.P', 'old_label': '18.cc1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.CC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264740
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.G', 'coset_action_label': None, 'count': 6, 'diagramx': [9081, -1, 8518, -1], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 51706588024878582378240, 10628652128248793890219496307613835949508, 418802671169936714973312003, 228938464225565425265821550127360, 526261674286189736370176755646672643, 17683942790150574557177061504243, 376703623296244, 180222528605051213902522335603064762218716], 'label': '708588.ir.18.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '18.cd1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.CD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264741
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '54.B', 'coset_action_label': None, 'count': 2, 'diagramx': [2939, -1, 5771, -1], 'generators': [51706588024878582378240, 5452012901627209662414261814, 17683942790150574557177061504243, 526261674286189736370176755646672643, 119047606003398925678629914726400, 376703623296244, 275960179627539264660514694801866760845588, 10628652128248793890219496307613835949508, 418802671169936714973312003, 297832896787709604644181405596151018847292], 'label': '708588.ir.18.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '18.ce1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.CE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264742
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '6.C', 'coset_action_label': None, 'count': 2, 'diagramx': [2149, 7928, 1676, 2493], 'generators': [6790345324355951192832502384381801104, 526270820517725416616431696011344784, 51706588024878582378240, 5452012901627209662414261814, 418802671169936714973312003, 119047606003398925678629914726400, 96030965731677069455593504544818913500805, 17683942790150574557177061504243, 138276680670356016853249968186779369783043, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.C', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264743
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '54.B', 'coset_action_label': None, 'count': 4, 'diagramx': [2277, -1, 5475, -1], 'generators': [287204516022283855598395152036701885791196, 51706588024878582378240, 10066262934746752030404593874, 17683942790150574557177061504243, 526261674286189736370176755646672643, 119047606003398925678629914726400, 376703623296244, 275960179627539264660514694801866760845588, 10628652128248793890219496307613835949508, 418802671169936714973312003], 'label': '708588.ir.18.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.H', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '18.cf1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.CF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264744
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '18.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '54.B', 'coset_action_label': None, 'count': 2, 'diagramx': [9761, -1, 8822, -1], 'generators': [51706588024878582378240, 17683942790150574557177061504243, 287204516178583945959068886222456540936719, 526261674286189736370176755646672643, 119047606003398925678629914726400, 376703623296244, 275960179627539264660514694801866760845588, 10628652128248793890219496307613835949508, 418802671169936714973312003, 138276680670356016853247656929952553164800], 'label': '708588.ir.18.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '18.cg1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.CG', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264745
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.A', 'coset_action_label': None, 'count': 27, 'diagramx': [1978, -1, 9816, -1], 'generators': [319120605543702796347517168439796380898725, 526270820517725416616431696011344784, 51706588024878582378240, 275962352999916311011770156949156061264640, 42545277067315780556434868261637774056155, 418802671169936714973312003, 17683942790150574557177061504243, 376703623296244, 4865804109758637364, 10628907036246685625578073782240332522387], 'label': '708588.ir.27.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.A', 'old_label': '27.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.A', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264746
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '972.A', 'coset_action_label': None, 'count': 54, 'diagramx': [2129, -1, 9883, -1], 'generators': [3530817441680106216413034541632764130, 526270820517725416616431696011344784, 287201001851975715875934014054735451025226, 418802671169936714973312003, 26980883647382640775204, 17683942790150574557177061504243, 138280195024437316275543138602901430222324, 4865804109758637364, 10628907036246685625578073782240332522387, 74458922054394411028098379591516066280276], 'label': '708588.ir.27.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.B', 'old_label': '27.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.B', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264747
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '972.A', 'coset_action_label': None, 'count': 54, 'diagramx': [2305, -1, 9962, -1], 'generators': [138276680780252778828862683476067478087203, 526270820517725416616431696011344784, 418802671169936714973312003, 51706588401582205674484, 4866515391209517504, 319114901546215009540532703490622578583491, 159556232672278924018461017628285849450812, 17683942790150574557177061504243, 109896310316162009746131359120164, 10628907036246685625578073782240332522387], 'label': '708588.ir.27.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.C', 'old_label': '27.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.C', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264748
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '972.A', 'coset_action_label': None, 'count': 54, 'diagramx': [1253, -1, 9492, -1], 'generators': [74456188888925260161861119794211475076295, 526270820517725416616431696011344784, 275960179627539264660514695136457042471043, 287204516178583945959068886222456540936719, 418802671169936714973312003, 51706588401582205674484, 4866515391209517504, 119047606003398925678629914726400, 17683942790150574557177061504243, 10628907036246685625578073782240332522387], 'label': '708588.ir.27.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.D', 'old_label': '27.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.D', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264749
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.C', 'coset_action_label': None, 'count': 18, 'diagramx': [291, -1, 9062, -1], 'generators': [526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 138280195015291053717442806397270548430323, 31911463630587598885715743912405539819359, 84490844629123685576258779161002885723045, 17683942790150574557177061504243, 376703623296244, 4865804109758637364, 10628907036246685625578073782240332522387], 'label': '708588.ir.27.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.B', 'old_label': '27.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.E', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264750
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': None, 'contains': None, 'core': '108.D', 'coset_action_label': None, 'count': 36, 'diagramx': [1612, -1, 9652, -1], 'generators': [329746541738778355955012995978380097860359, 51706588024878582378240, 3785798708645587997719919976419166964, 17683942790150574557177061504243, 287201001761025634705489882684698310502879, 376703623296244, 10628907036246685625578073782240332522387, 526270820517725416616431696011344784, 418802671169936714973312003, 275960179718500734264803501521575448197268], 'label': '708588.ir.27.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.B', 'old_label': '27.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.F', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264751
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.E', 'coset_action_label': None, 'count': 18, 'diagramx': [1810, -1, 9741, -1], 'generators': [526270820517725416616431696011344784, 51706588024878582378240, 6790253125346841453596757796579269810, 418802671169936714973312003, 138280195015291053717442806397270548430323, 74458922054394023272575312327973798952279, 17683942790150574557177061504243, 376703623296244, 307867297784748005762243334573054653329466, 10628907036246685625578073782240332522387], 'label': '708588.ir.27.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.B', 'old_label': '27.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.G', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264752
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '972.A', 'coset_action_label': None, 'count': 54, 'diagramx': [1066, -1, 9408, -1], 'generators': [138276680771715517399483612107375766086964, 17683942790150574557177061504243, 74455917535249672263434671931082479773895, 26980883647382640775204, 10628907036246685625578073782240332522387, 138273964847675931875301272455087819690803, 526270820517725416616431696011344784, 418802671169936714973312003, 4865804109758637364, 170184613630012996506929348731808078545469], 'label': '708588.ir.27.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.H', 'old_label': '27.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.H', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264753
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': None, 'contains': None, 'core': '6.D', 'coset_action_label': None, 'count': 4, 'diagramx': [1652, 5697, 1454, 2136], 'generators': [6790345324355951192832502384381801104, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 10066262934746752030404593874, 119047606003398925678629914726400, 17683942790150574557177061504243, 138276680670356016853249968186779369783043, 376703623296244, 96030965723140195781737500439669476086549, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.D', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264754
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.B', 'coset_action_label': None, 'count': 9, 'diagramx': [98, -1, 8975, -1], 'generators': [51706588024878582378240, 17683942790150574557177061504243, 138276680780252778828862683476067478087203, 376703623296244, 10628907036246685625578073782240332522387, 74459176962387657409917560207599480811399, 526270820517725416616431696011344784, 418802671169936714973312003, 4865804109758637364, 170184613630012996506929348731808078545469], 'label': '708588.ir.27.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.C', 'old_label': '27.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.I', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264755
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.G', 'coset_action_label': None, 'count': 9, 'diagramx': [727, -1, 9257, -1], 'generators': [138276680780252778828862683476067478087203, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 228938464225565425265821550127360, 339780671217313013210136813049930894724852, 17683942790150574557177061504243, 376703623296244, 180222528605051213902522335603064762218716, 10628907036246685625578073782240332522387], 'label': '708588.ir.27.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.C', 'old_label': '27.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.J', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264756
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.I', 'coset_action_label': None, 'count': 18, 'diagramx': [504, -1, 9157, -1], 'generators': [138276680780252778828862683476067478087203, 526270820517725416616431696011344784, 51706588024878582378240, 170184613437704673061999269732179767146956, 127579446523388019500445797913843, 418802671169936714973312003, 339781197478987299399868317422576782644211, 17683942790150574557177061504243, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.27.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.C', 'old_label': '27.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.K', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264757
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '54.B', 'coset_action_label': None, 'count': 3, 'diagramx': [906, -1, 9336, -1], 'generators': [74456188888925647966837907823060756107252, 526270820517725416616431696011344784, 51706588024878582378240, 287204516178583945959068886222456540936719, 418802671169936714973312003, 119047606003398925678629914726400, 17683942790150574557177061504243, 376703623296244, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.27.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.D', 'old_label': '27.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.L', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264758
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '27.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '54.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1429, -1, 9571, -1], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 339786375214812091638666253706205574352611, 17683942790150574557177061504243, 376703623296244, 170184613630012996506929348731808078545469, 10628907036246685625578073782240332522387], 'label': '708588.ir.27.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '27.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.M', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264759
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '36.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2011, -1, 5391], 'generators': [138280195015291053717442806397270548430323, 51706588024878582378240, 17684330570401657831907612774644, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 418802671169936714973312003, 4865804109758637364, 3530817442067886467495597735425301634], 'label': '708588.ir.36.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.A', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264760
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '36.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1099, -1, 5245], 'generators': [138276680780252778828862683476067478087203, 17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 526261674286189736370176755646672643, 376703623296244, 4865804109758637364, 10628907036246685625578073782240332522387, 138273964847675931875301272455087819690803], 'label': '708588.ir.36.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.b1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.B', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264761
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '36.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2923, -1, 5537], 'generators': [138276680780252778828862683476067478087203, 17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 127579446523390330757272614416164, 526261674286189736370176755646672643, 376703623296244, 4865804109758637364, 10628907036246685625578073782240332522387], 'label': '708588.ir.36.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.c1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.C', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264762
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '36.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.D', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3834, -1, 5683], 'generators': [17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 376703623296244, 4865804109758637364, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.36.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.d1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.D', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264763
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '36.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': None, 'contains': None, 'core': '36.E', 'coset_action_label': None, 'count': 4, 'diagramx': [-1, 4746, -1, 5829], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 17684330570401657831907612774644, 51706588024878582378240, 127579446523388019500445797913843, 418802671169936714973312003, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.36.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.e1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.E', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264764
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.E', 'coset_action_label': None, 'count': 1, 'diagramx': [825, 2351, 1084, 1601], 'generators': [526270820517725416616431696011344784, 51706588024878582378240, 275962352999916311011770156949156061264640, 42545277067315780556434868261637774056155, 418802671169936714973312003, 119047606003398925678629914726400, 17683942790150574557177061504243, 376703623296244, 4865804109758637364, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.E', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264765
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '36.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.F', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 6568, -1, 6120], 'generators': [17684330570401657831907612774644, 51706588024878582378240, 275962352999916311011767845692341698688004, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 376703623296244, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.36.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.f1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.F', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264766
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '36.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.G', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 8391, -1, 6412], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 228938464225565425265821550127360, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.36.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.g1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.G', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264767
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '36.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.H', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 7480, -1, 6266], 'generators': [17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 138276680670357275095627799925965150714403, 376703623296244, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.36.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.H', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.h1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.H', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264768
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '36.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.I', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5657, -1, 5975], 'generators': [6790345324355951192832502384381801104, 17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 138276680670356016853249968186779369783043, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.36.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.I', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.i1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.I', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264769
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '54.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '78732.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '54.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1126, -1, 6563], 'generators': [138276680780252778828862683476067478087203, 74456188888925647966837907823060756107252, 17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 138273964847675931875301272455087819690803], 'label': '708588.ir.54.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '54.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '54.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.A', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264770
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '54.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '78732.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '54.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2100, -1, 6719], 'generators': [17684330570401657831907612774644, 51706588024878582378240, 287204516178583945959068886222456540936719, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 376703623296244, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.54.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '54.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '54.b1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.B', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264771
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '108.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5548, -1, 7589], 'generators': [275962352999916311011770156949156061264640, 51706588024878582378240, 17684330570401657831907612774644, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 418802671169936714973312003, 4865804109758637364], 'label': '708588.ir.108.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '108.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.A', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264772
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '108.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6316, -1, 7712], 'generators': [138276680780252778828862683476067478087203, 17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 526261674286189736370176755646672643, 376703623296244, 4865804109758637364, 10628907036246685625578073782240332522387], 'label': '708588.ir.108.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '108.b1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.B', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264773
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '108.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.C', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 7085, -1, 7835], 'generators': [138280195015291053717442806397270548430323, 51706588024878582378240, 17684330570401657831907612774644, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 418802671169936714973312003, 4865804109758637364], 'label': '708588.ir.108.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '108.c1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.C', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264774
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '108.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': None, 'contains': None, 'core': '108.D', 'coset_action_label': None, 'count': 4, 'diagramx': [-1, 1058, -1, 6870], 'generators': [17684330570401657831907612774644, 3530817442067886464941050707791135318, 51706588024878582378240, 418802671169936714973312003, 138280195015291053717442806397270548430323, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.108.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '108.d1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.D', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264775
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.F', 'coset_action_label': None, 'count': 1, 'diagramx': [659, 1235, 1010, 1422], 'generators': [6790345324355951192832502384381801104, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 119047606003398925678629914726400, 17683942790150574557177061504243, 138276680670356016853249968186779369783043, 4865804109758637364, 376703623296244, 170184613630012996506929348731808078545469, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.F', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264776
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '108.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.E', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2881, -1, 7162], 'generators': [138280195015291053717442806397270548430323, 51706588024878582378240, 17684330570401657831907612774644, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 418802671169936714973312003, 6790253125346841453596757796579269810], 'label': '708588.ir.108.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '108.e1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.E', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264777
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '108.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.F', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1970, -1, 7016], 'generators': [138276680780252778828862683476067478087203, 17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 138273964847675931875301272455087819690803], 'label': '708588.ir.108.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '108.f1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.F', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264778
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '108.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.G', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3793, -1, 7308], 'generators': [138276680780252778828862683476067478087203, 17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 228938464225565425265821550127360, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.108.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '108.g1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.G', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264779
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '108.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '108.H', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4704, -1, 7454], 'generators': [17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 119047606003398925678629914726400, 526261674286189736370176755646672643, 376703623296244, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.108.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.H', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '108.h1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.H', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264780
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '108.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '108.I', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 7928, -1, 7970], 'generators': [138276680780252778828862683476067478087203, 17684330570401657831907612774644, 51706588024878582378240, 127579446523388019500445797913843, 418802671169936714973312003, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.108.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '108.I', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '108.i1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.I', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264781
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '324.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '324.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 881, -1, 8088], 'generators': [51706588024878582378240, 17684330570401657831907612774644, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 418802671169936714973312003, 4865804109758637364], 'label': '708588.ir.324.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '324.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.A', 'subgroup_fusion': None, 'weyl_group': '324.167'}
    • id: 244264782
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '324.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '324.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2317, -1, 8317], 'generators': [51706588024878582378240, 17684330570401657831907612774644, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 418802671169936714973312003, 138276680670357275095627799925965150714403], 'label': '708588.ir.324.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '324.b1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.B', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264783
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '324.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '324.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3854, -1, 8563], 'generators': [138276680780252778828862683476067478087203, 17684330570401657831907612774644, 51706588024878582378240, 418802671169936714973312003, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.324.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '324.c1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.C', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264784
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '324.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '324.D', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 3085, -1, 8440], 'generators': [51706588024878582378240, 17684330570401657831907612774644, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 418802671169936714973312003, 275960179718500734264803501521575448197268], 'label': '708588.ir.324.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '324.d1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.D', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264785
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '324.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8748.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '324.E', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1548, -1, 8194], 'generators': [17684330570401657831907612774644, 51706588024878582378240, 275962352999916311011767845692341698688004, 418802671169936714973312003, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.324.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '324.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '324.e1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.E', 'subgroup_fusion': None, 'weyl_group': '8748.ko'}
    • id: 244264786
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.G', 'coset_action_label': None, 'count': 1, 'diagramx': [1983, 6813, 1602, 2315], 'generators': [6790345324355951192832502384381801104, 526270820517725416616431696011344784, 51706588024878582378240, 5452012901627209662414261814, 418802671169936714973312003, 119047606003398925678629914726400, 17683942790150574557177061504243, 138276680670356016853249968186779369783043, 376703623296244, 180222528605051213902522335603064762218716, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.G', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264787
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '972.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '972.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 841, -1, 8670], 'generators': [17684330570401657831907612774644, 526261674286189736370176755646672643, 26980883647382640775204, 10628907036246685625578073782240332522387, 418802671169936714973312003, 4865804109758637364], 'label': '708588.ir.972.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '972.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '972.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.A', 'subgroup_fusion': None, 'weyl_group': '324.167'}
    • id: 244264788
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '972.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '972.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1399, -1, 8759], 'generators': [51706588024878582378240, 17684330570401657831907612774644, 526261674286189736370176755646672643, 376703623296244, 10628907036246685625578073782240332522387, 418802671169936714973312003], 'label': '708588.ir.972.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '972.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '972.b1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.B', 'subgroup_fusion': None, 'weyl_group': '324.167'}
    • id: 244264789
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '2916.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2916.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1399, -1, 8937], 'generators': [17684330570401657831907612774644, 526261674286189736370176755646672643, 10628907036246685625578073782240332522387, 26978572390555824272883, 418802671169936714973312003], 'label': '708588.ir.2916.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2916.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2916.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.A', 'subgroup_fusion': None, 'weyl_group': '324.167'}
    • id: 244264790
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '2916.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '324.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2916.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 841, -1, 8849], 'generators': [17684330570401657831907612774644, 526261674286189736370176755646672643, 26980883647382640775204, 10628907036246685625578073782240332522387, 418802671169936714973312003], 'label': '708588.ir.2916.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2916.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2916.b1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.B', 'subgroup_fusion': None, 'weyl_group': '324.167'}
    • id: 244264791
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '8748.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '8748.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 800, -1, 9027], 'generators': [17684330570401657831907612774644, 526261674286189736370176755646672643, 10628907036246685625578073782240332522387, 418802671169936714973312003], 'label': '708588.ir.8748.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8748.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '8748.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8748.A', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 244264792
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '26244.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '26244.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 800, -1, 9116], 'generators': [10628907036246266822906903845525359210384, 17683942790150574557177061504243, 526261674673969987453451486197943044], 'label': '708588.ir.26244.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '26244.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '26244.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '26244.A', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 244264793
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '26244.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '26244.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1915, -1, 9295], 'generators': [17684330570401657831907612774644, 526261674286189736370176755646672643, 10628907036246685625578073782240332522387], 'label': '708588.ir.26244.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '26244.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '26244.b1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '26244.B', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 244264794
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '26244.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '26244.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1357, -1, 9205], 'generators': [17684330570401657831907612774644, 10628907036246685625578073782240332522387, 526261674673969987453451486197943044], 'label': '708588.ir.26244.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '26244.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '26244.c1.N', 'projective_image': '708588.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '26244.C', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 244264795
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '78732.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '78732.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 759, -1, 9384], 'generators': [526279357391374544604860502761552880, 10628652128248793890219496307613835949508], 'label': '708588.ir.78732.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '78732.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '78732.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '78732.A', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 244264796
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '78732.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '78732.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1317, -1, 9473], 'generators': [17683942790150574557177061504243, 10628652128248793890219496307613835949508], 'label': '708588.ir.78732.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '78732.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '78732.b1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '78732.B', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 244264797
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '6.H', 'coset_action_label': None, 'count': 2, 'diagramx': [2845, 9275, 1988, 2709], 'generators': [6790345324355951192832502384381801104, 526270820517725416616431696011344784, 51706588024878582378240, 170184613437704673061999269732179767146956, 418802671169936714973312003, 10066262934746752030404593874, 119047606003398925678629914726400, 17683942790150574557177061504243, 138276680670356016853249968186779369783043, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.H', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.H', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264798
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '78732.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '78732.C', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2432, -1, 9652], 'generators': [10628907044783947054957145485777634000884, 526261674673969987453451486197943044], 'label': '708588.ir.78732.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '78732.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '78732.c1.N', 'projective_image': '708588.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '78732.C', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 244264799
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '78732.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '78732.D', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1875, -1, 9563], 'generators': [17684330570401657831907612774644, 10628907036246685625578073782240332522387], 'label': '708588.ir.78732.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '78732.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '78732.d1.N', 'projective_image': '708588.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '78732.D', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 244264800
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '177147.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '708588.a1', 'coset_action_label': None, 'count': 6561, 'diagramx': None, 'generators': [52577759690941884690914678496719036016029, 84494104065418839069282651946550593118036], 'label': '708588.ir.177147.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '177147.a1', 'projective_image': '708588.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '177147.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 244264801
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '236196.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '236196.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1704, -1, 9893], 'generators': [10628652128248793890219496307613835949508], 'label': '708588.ir.236196.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '236196.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '236196.a1.N', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '236196.A', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 244264802
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '236196.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '236196.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 725, -1, 9736], 'generators': [10628907036246685625578073782240332522387], 'label': '708588.ir.236196.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '236196.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '236196.b1.N', 'projective_image': '708588.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '236196.B', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 244264803
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '236196.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '236196.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1214, -1, 9814], 'generators': [10628652136785279759096401461690034887203], 'label': '708588.ir.236196.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '236196.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '236196.c1.N', 'projective_image': '708588.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '236196.C', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 244264804
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '708588.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '708588.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 725, -1, 9971], 'generators': [], 'label': '708588.ir.708588.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '708588.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '708588.a1.N', 'projective_image': '708588.ir', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '708588.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 244264805
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2480, -1, 1824, -1], 'generators': [526270820517725416616431696011344784, 228928849727747192390570990590324, 51706588024878582378240, 275962352852763322624190262895615342506694, 418802671169936714973312003, 17683942790150574557177061504243, 376703623296244, 4865804109758637364, 74459448316068278439886730038647718997636, 10628907036246685625578073782240332522387, 138273964847675931875301272455087819690803], 'label': '708588.ir.6.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.I', 'old_label': '6.i1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.I', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264806
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1155, -1, 1232, -1], 'generators': [138276680780252778828862683476067478087203, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 127579446523390330757272614416164, 17683942790150574557177061504243, 96030965731677069455593504544818913500805, 376703623296244, 4865804109758637364, 10628907036246685625578073782240332522387, 138273964847675931875301272455087819690803], 'label': '708588.ir.6.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '6.j1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.J', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264807
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '2.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2.A', 'coset_action_label': None, 'count': 2, 'diagramx': [93, 1235, 117, 281], 'generators': [6790345324355951192832502384381801104, 51706588024878582378240, 526261674673969987453451486197943044, 418802671169936714973312003, 119047606003398925678629914726400, 96030965731677069455593504544818913500805, 17683942790150574557177061504243, 4865804109758637364, 138276680670356016853249968186779369783043, 376703623296244, 10628907044783947054957145485777634000884, 10066262937301299313346728917], 'label': '708588.ir.2.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.A', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264808
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.B', 'coset_action_label': None, 'count': 6, 'diagramx': [990, -1, 1158, -1], 'generators': [526270820517725416616431696011344784, 51706588024878582378240, 275962352999916311011770156949156061264640, 418802671169936714973312003, 119047606003398925678629914726400, 96030965731677069455593504544818913500805, 17683942790150574557177061504243, 376703623296244, 4865804109758637364, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.D', 'old_label': '6.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.K', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264809
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '18.A', 'coset_action_label': None, 'count': 4, 'diagramx': [260, -1, 831, -1], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 371989804195597658810391960246407528040385, 17683942790150574557177061504243, 376703623296244, 4865804109758637364, 10066262937301299313346728917, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '6.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.L', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264810
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 4, 'contained_in': None, 'contains': None, 'core': '18.B', 'coset_action_label': None, 'count': 8, 'diagramx': [2645, -1, 1898, -1], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 228934301664216768977495101939798, 228928849727747192390570990590324, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 371989804195597658810391960246407528040385, 17683942790150574557177061504243, 376703623296244, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '6.m1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.M', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264811
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '18.C', 'coset_action_label': None, 'count': 4, 'diagramx': [1817, -1, 1528, -1], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 228934301664216768977495101939798, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 233718827641170969604125301755226769444642, 17683942790150574557177061504243, 376703623296244, 10628907036246685625578073782240332522387, 10066262937301299313346728917], 'label': '708588.ir.6.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '6.n1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.N', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264812
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.C', 'coset_action_label': None, 'count': 6, 'diagramx': [3278, -1, 2181, -1], 'generators': [138276680780252778828862683476067478087203, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 127579446523390330757272614416164, 159556232672278924018461017628285849450812, 17683942790150574557177061504243, 376703623296244, 4865804109758637364, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '6.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.O', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264813
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 6, 'diagramx': [93, -1, 757, -1], 'generators': [6790345324355951192832502384381801104, 138276680780252778828862683476067478087203, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 127579446523390330757272614416164, 159556232672278924018461017628285849450812, 17683942790150574557177061504243, 376703623296244, 4865804109758637364, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '6.p1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.P', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264814
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '18.E', 'coset_action_label': None, 'count': 2, 'diagramx': [2314, -1, 1750, -1], 'generators': [4865804109758637364, 376703623296244, 418802671169936714973312003, 10066262937301299313346728917, 10628907036246685625578073782240332522387, 275960179627539264660514694801866760845588, 307870811955056145406024420522603476319436, 17683942790150574557177061504243, 526270820517725416616431696011344784, 119047606003398925678629914726400, 51706588024878582378240], 'label': '708588.ir.6.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '6.q1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.Q', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264815
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '18.F', 'coset_action_label': None, 'count': 4, 'diagramx': [459, -1, 920, -1], 'generators': [526270820517725416616431696011344784, 51706588024878582378240, 275962352999916311011770156949156061264640, 42545277067315780556434868261637774056155, 418802671169936714973312003, 119047606003398925678629914726400, 17683942790150574557177061504243, 376703623296244, 138276680670356016853247656929952553164800, 275960179627539264660514694801866760845588, 10628907036246685625578073782240332522387], 'label': '708588.ir.6.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '6.r1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.R', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264816
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '6.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '18.G', 'coset_action_label': None, 'count': 2, 'diagramx': [3078, -1, 2092, -1], 'generators': [376703623296244, 418802671169936714973312003, 10066262937301299313346728917, 138276680670356016853247656929952553164800, 10628907036246685625578073782240332522387, 275960179627539264660514694801866760845588, 307870811955056145406024420522603476319436, 17683942790150574557177061504243, 526270820517725416616431696011344784, 119047606003398925678629914726400, 51706588024878582378240], 'label': '708588.ir.6.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '6.s1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.S', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264817
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '9.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '9.A', 'coset_action_label': None, 'count': 1, 'diagramx': [795, 1201, 2571, 2924], 'generators': [6790345324355951192832502384381801104, 74456188888925647966837907823060756107252, 526270820517725416616431696011344784, 51706588024878582378240, 418802671169936714973312003, 119047606003398925678629914726400, 17683942790150574557177061504243, 138276680670356016853249968186779369783043, 376703623296244, 170184613630012996506929348731808078545469, 10628907036246685625578073782240332522387], 'label': '708588.ir.9.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '9.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '9.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.A', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 244264818
      {'ambient': '708588.ir', 'aut_centralizer_order': None, 'aut_label': '2.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2.B', 'coset_action_label': None, 'count': 1, 'diagramx': [276, 2460, 198, 477], 'generators': [6790345324355951192832502384381801104, 51706588024878582378240, 526261674673969987453451486197943044, 418802671169936714973312003, 119047606003398925678629914726400, 159556232672278924018461017628285849450812, 17683942790150574557177061504243, 4865804109758637364, 138276680670356016853249968186779369783043, 376703623296244, 10628907044783947054957145485777634000884, 10066262937301299313346728917], 'label': '708588.ir.2.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.B', 'subgroup_fusion': None, 'weyl_group': None}