Formats: - HTML - YAML - JSON - 2026-07-25T09:30:14.489996
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [2, 8, 6, 3, 3, 3, 3], 'aut_gens': [[1, 6, 48, 144, 432, 1296], [701, 1842, 624, 3744, 1296, 432], [2801, 3462, 3600, 624, 1728, 2160], [2837, 2694, 480, 1872, 864, 2592], [1489, 1254, 48, 144, 432, 1296], [2161, 6, 480, 3600, 432, 1296], [2593, 1302, 48, 144, 432, 1296], [1297, 2166, 48, 144, 432, 1296]], 'aut_group': '7776.cw', 'aut_hash': 8212187940285761847, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7776, 'aut_permdeg': 216, 'aut_perms': [3158506457474230433459792849847070923855406099744454495826174004841063922807674570758338694611342546222006281385707425380578383933896785867766422440009553615560866760767547274128920319501041178165410687700855342954644626435657228472608800381263652498468789382070001679892316375475998898638594852934317109477026378315889386550774302482655478473811459073099369512835158035172381387582440134245843233659250040882579, 7224324764286432262959655758446809664413354120332710114096244300756486421170630402182304128065825251603977116938003988596752424715248379883688489510241635573357259227911422446380844901116040829380884614100679321353431170697784939327521213543118320962647371751642638730014854503639580247928799928665839497464444047775914337457843900621846620691571752592331019689218576182067264958249073212439787296754375872890445, 6048047708346898465648736728563601176563086165605119339002431603159906149215754302185893112042391179128856248086495503250830478847075974159771565352789275488422894124549731381772495445318651507121693617966762803614782570411400649597451378238625008651026742016716835966012351391809678967236673608855241848362944452501214264307232452989174512749078626786414108406494714306541512455492519318191202812991894303218487, 7369629689363071332578164811420688879771355445538884698847178708082186135959990240219553329838077259217018810464595687700531605949906956871577954183839187852509565898374382372396037957082479431302789659838147948388047576126679148849808558729510171519563363614544872525384518727715691049800437999986167127761723501335851724500656307245905708591586997371937135960854921800627971395267590482268313064751137607624405, 34710597567374543182397843164060418128730439144037943108347752625334938570632458418597685844343761666187273287527860801288856589090470270024045907500877121486735699820917110353000123781369454431870091921754447402901172663276652122939959626267352827933342677613977510395876245833212035250840907751307735628746556110574846851131118055138930237151483106147008871009353003530715621703393979888203070816125350332414, 6937140360292110861289582481283651600894251136995116995519854206625273248406318122762074595542060777295505003041046543335214003645005038990381533202140510963502682054278328701066244569379178874575011581693712003744178637185345471444698376161556226410342569876333029952714390371115670906454895440874681211531861897793612869284070986603601457980602058487072395410698803079723067493852671646951691044109215774450, 34733789135498519726860218319374080379093253588396550927177307088226037315242627977431289766571039764453186765610746136632884524528233054144039259754723452246708256638737636076890970235801343517073779707649201354659204626375612078697106188278385726087349549699004861526431881439396895121045026436991730409692343786364015182866448856456940687367610195846128171749959800446844381242441373164992358366610070336326], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 81, 1, 1], [3, 8, 1, 1], [3, 9, 2, 1], [3, 24, 1, 1], [3, 48, 1, 1], [3, 72, 2, 1], [4, 162, 1, 1], [4, 324, 1, 1], [6, 72, 1, 1], [6, 81, 2, 1], [6, 108, 2, 1], [6, 216, 1, 1], [6, 216, 2, 1], [8, 162, 1, 2], [12, 162, 2, 1], [12, 324, 2, 1], [24, 162, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:(S_3\\times \\SD_{16})', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '7776.cw', 'autcentquo_hash': 8212187940285761847, 'autcentquo_nilpotent': False, 'autcentquo_order': 7776, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:(S_3\\times \\SD_{16})', 'cc_stats': [[1, 1, 1], [2, 36, 1], [2, 81, 1], [3, 8, 1], [3, 9, 2], [3, 24, 1], [3, 48, 1], [3, 72, 2], [4, 162, 1], [4, 324, 1], [6, 72, 1], [6, 81, 2], [6, 108, 2], [6, 216, 3], [8, 162, 2], [12, 162, 2], [12, 324, 2], [24, 162, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '3888.el', 'commutator_count': 1, 'commutator_label': '324.164', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 116, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 81, 1, 1], [3, 8, 1, 1], [3, 9, 2, 1], [3, 24, 1, 1], [3, 48, 1, 1], [3, 72, 2, 1], [4, 162, 1, 1], [4, 324, 1, 1], [6, 72, 1, 1], [6, 81, 2, 1], [6, 108, 2, 1], [6, 216, 1, 1], [6, 216, 2, 1], [8, 162, 2, 1], [12, 162, 2, 1], [12, 324, 2, 1], [24, 162, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 576, 'exponent': 24, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 2], [48, 1, 1]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '432.737', 'hash': 401516246772182357, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [6, 8, 3, 3, 3, 3], 'inner_gens': [[1, 2562, 480, 1632, 432, 2592], [565, 6, 3792, 960, 2160, 3456], [865, 1878, 48, 144, 432, 1296], [2977, 630, 48, 144, 432, 1296], [1, 3462, 48, 144, 432, 1296], [2593, 3030, 48, 144, 432, 1296]], 'inner_hash': 401516246772182357, 'inner_nilpotent': False, 'inner_order': 3888, 'inner_split': True, 'inner_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'inner_used': [1, 2], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 12], [2, 9], [8, 6], [24, 2], [48, 1]], 'label': '3888.el', 'linC_count': 2, 'linC_degree': 24, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 24, 'linQ_degree_count': 2, 'linQ_dim': 24, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 24, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^4:(C3*SD16)', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 21, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 30, 'number_divisions': 19, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 154, 'number_subgroup_classes': 155, 'number_subgroups': 7491, 'old_label': None, 'order': 3888, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 117], [3, 242], [4, 486], [6, 1098], [8, 324], [12, 972], [24, 648]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[53, 3030, 480, 1872, 864, 2592]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 2], [8, 3], [16, 2], [24, 2], [48, 1]], 'representations': {'PC': {'code': '4989780134592565964713441398636317857461685543012572903840059522373386598741556586794652666712204800432783', 'gens': [1, 3, 6, 7, 8, 9], 'pres': [9, -2, -3, -2, -2, -2, -3, 3, -3, 3, 18, 69176, 31196, 74, 34131, 58980, 102, 128524, 51313, 25925, 24638, 34151, 17312, 257, 102822, 58983, 10104, 5829, 798, 25945, 7810, 2635, 209960, 46682, 5867, 8792]}, 'Perm': {'d': 27, 'gens': [8806515351680094219438534102, 6257545204994460878675312196]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:(C_3\\times \\SD_{16})', 'transitive_degree': 27, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    • id: 161031386
      {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 116, 'group_order': 3888, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 161031397
      {'aut_label': '2A', 'centralizer': '36.b1.a1', 'counter': 2, 'group_counter': 116, 'group_order': 3888, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 3219, 'size': 36}
    • id: 161031408
      {'aut_label': '2B', 'centralizer': '81.a1.a1', 'counter': 3, 'group_counter': 116, 'group_order': 3888, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 2376, 'size': 81}
    • id: 161031410
      {'aut_label': '3A', 'centralizer': '8.b1.a1', 'counter': 4, 'group_counter': 116, 'group_order': 3888, 'label': '3A', 'order': 3, 'powers': [4, 1], 'representative': 2592, 'size': 8}
    • id: 161031411
      {'aut_label': '3B1', 'centralizer': '9.a1.a1', 'counter': 5, 'group_counter': 116, 'group_order': 3888, 'label': '3B1', 'order': 3, 'powers': [6, 1], 'representative': 3554, 'size': 9}
    • id: 161031412
      {'aut_label': '3B1', 'centralizer': '9.a1.a1', 'counter': 6, 'group_counter': 116, 'group_order': 3888, 'label': '3B-1', 'order': 3, 'powers': [5, 1], 'representative': 2212, 'size': 9}
    • id: 161031413
      {'aut_label': '3C', 'centralizer': '24.e1.a1', 'counter': 7, 'group_counter': 116, 'group_order': 3888, 'label': '3C', 'order': 3, 'powers': [7, 1], 'representative': 480, 'size': 24}
    • id: 161031414
      {'aut_label': '3D', 'centralizer': '48.a1.a1', 'counter': 8, 'group_counter': 116, 'group_order': 3888, 'label': '3D', 'order': 3, 'powers': [8, 1], 'representative': 1440, 'size': 48}
    • id: 161031415
      {'aut_label': '3E1', 'centralizer': '72.e1.a1', 'counter': 9, 'group_counter': 116, 'group_order': 3888, 'label': '3E1', 'order': 3, 'powers': [10, 1], 'representative': 1012, 'size': 72}
    • id: 161031387
      {'aut_label': '3E1', 'centralizer': '72.e1.a1', 'counter': 10, 'group_counter': 116, 'group_order': 3888, 'label': '3E-1', 'order': 3, 'powers': [9, 1], 'representative': 2882, 'size': 72}
    • id: 161031388
      {'aut_label': '4A', 'centralizer': '162.c1.a1', 'counter': 11, 'group_counter': 116, 'group_order': 3888, 'label': '4A', 'order': 4, 'powers': [3, 11], 'representative': 2340, 'size': 162}
    • id: 161031389
      {'aut_label': '4B', 'centralizer': '324.e1.a1', 'counter': 12, 'group_counter': 116, 'group_order': 3888, 'label': '4B', 'order': 4, 'powers': [3, 12], 'representative': 1701, 'size': 324}
    • id: 161031390
      {'aut_label': '6A', 'centralizer': '72.a1.a1', 'counter': 13, 'group_counter': 116, 'group_order': 3888, 'label': '6A', 'order': 6, 'powers': [4, 2], 'representative': 411, 'size': 72}
    • id: 161031391
      {'aut_label': '6B1', 'centralizer': '81.a1.a1', 'counter': 14, 'group_counter': 116, 'group_order': 3888, 'label': '6B1', 'order': 6, 'powers': [5, 3], 'representative': 172, 'size': 81}
    • id: 161031392
      {'aut_label': '6B1', 'centralizer': '81.a1.a1', 'counter': 15, 'group_counter': 116, 'group_order': 3888, 'label': '6B-1', 'order': 6, 'powers': [6, 3], 'representative': 2858, 'size': 81}
    • id: 161031393
      {'aut_label': '6C1', 'centralizer': '108.a1.a1', 'counter': 16, 'group_counter': 116, 'group_order': 3888, 'label': '6C1', 'order': 6, 'powers': [6, 2], 'representative': 2309, 'size': 108}
    • id: 161031394
      {'aut_label': '6C1', 'centralizer': '108.a1.a1', 'counter': 17, 'group_counter': 116, 'group_order': 3888, 'label': '6C-1', 'order': 6, 'powers': [5, 2], 'representative': 673, 'size': 108}
    • id: 161031395
      {'aut_label': '6D', 'centralizer': '216.b1.a1', 'counter': 18, 'group_counter': 116, 'group_order': 3888, 'label': '6D', 'order': 6, 'powers': [7, 2], 'representative': 147, 'size': 216}
    • id: 161031396
      {'aut_label': '6E1', 'centralizer': '216.c1.a1', 'counter': 19, 'group_counter': 116, 'group_order': 3888, 'label': '6E1', 'order': 6, 'powers': [9, 2], 'representative': 569, 'size': 216}
    • id: 161031398
      {'aut_label': '6E1', 'centralizer': '216.c1.a1', 'counter': 20, 'group_counter': 116, 'group_order': 3888, 'label': '6E-1', 'order': 6, 'powers': [10, 2], 'representative': 1573, 'size': 216}
    • id: 161031399
      {'aut_label': '8A1', 'centralizer': '162.c1.a1', 'counter': 21, 'group_counter': 116, 'group_order': 3888, 'label': '8A1', 'order': 8, 'powers': [11, 21], 'representative': 426, 'size': 162}
    • id: 161031400
      {'aut_label': '8A-1', 'centralizer': '162.c1.a1', 'counter': 22, 'group_counter': 116, 'group_order': 3888, 'label': '8A-1', 'order': 8, 'powers': [11, 22], 'representative': 3318, 'size': 162}
    • id: 161031401
      {'aut_label': '12A1', 'centralizer': '162.c1.a1', 'counter': 23, 'group_counter': 116, 'group_order': 3888, 'label': '12A1', 'order': 12, 'powers': [14, 11], 'representative': 974, 'size': 162}
    • id: 161031402
      {'aut_label': '12A1', 'centralizer': '162.c1.a1', 'counter': 24, 'group_counter': 116, 'group_order': 3888, 'label': '12A-1', 'order': 12, 'powers': [15, 11], 'representative': 3832, 'size': 162}
    • id: 161031403
      {'aut_label': '12B1', 'centralizer': '324.e1.a1', 'counter': 25, 'group_counter': 116, 'group_order': 3888, 'label': '12B1', 'order': 12, 'powers': [14, 12], 'representative': 1871, 'size': 324}
    • id: 161031404
      {'aut_label': '12B1', 'centralizer': '324.e1.a1', 'counter': 26, 'group_counter': 116, 'group_order': 3888, 'label': '12B-1', 'order': 12, 'powers': [15, 12], 'representative': 1843, 'size': 324}
    • id: 161031405
      {'aut_label': '24A1', 'centralizer': '162.c1.a1', 'counter': 27, 'group_counter': 116, 'group_order': 3888, 'label': '24A1', 'order': 24, 'powers': [23, 21], 'representative': 322, 'size': 162}
    • id: 161031406
      {'aut_label': '24A-1', 'centralizer': '162.c1.a1', 'counter': 28, 'group_counter': 116, 'group_order': 3888, 'label': '24A-1', 'order': 24, 'powers': [24, 22], 'representative': 2708, 'size': 162}
    • id: 161031407
      {'aut_label': '24A-1', 'centralizer': '162.c1.a1', 'counter': 29, 'group_counter': 116, 'group_order': 3888, 'label': '24A7', 'order': 24, 'powers': [23, 22], 'representative': 2134, 'size': 162}
    • id: 161031409
      {'aut_label': '24A1', 'centralizer': '162.c1.a1', 'counter': 30, 'group_counter': 116, 'group_order': 3888, 'label': '24A-7', 'order': 24, 'powers': [24, 21], 'representative': 3152, 'size': 162}
  • gps_qchar • Show schema
    • id: 15863859
      {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 15863870
      {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 15863871
      {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 15863872
      {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 15863873
      {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 15863874
      {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.1f', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -1, -1, 2, 2, -1, -1, 2, -2, -2, -1, -1, 1, 1, -2, 1, 1, 2, 2, -1, -1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
    • id: 15863875
      {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, 2, 2, -1, -1, 2, 2, -1, -1, 2, 2, -2, -1, -1, 1, 1, -2, 1, 1, -2, -2, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 15863876
      {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, 2, -1, -1, 2, -2, 2, -1, -1, -1, -1, 2, -1, -1, -2, -2, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
    • id: 15863877
      {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, 0, 2, 2, 2, 2, 2, 2, 2, 2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863860
      {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.2b', 'multiplicity': 2, 'nt': [8, 8], 'qdim': 4, 'qvalues': [4, 0, -4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863861
      {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.2c', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, 0, 4, 4, -2, -2, 4, 4, -2, -2, -4, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863862
      {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.2d', 'multiplicity': 4, 'nt': [24, 41], 'qdim': 8, 'qvalues': [8, 0, -8, 8, -4, -4, 8, 8, -4, -4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863863
      {'cdim': 8, 'counter': 13, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.8a', 'multiplicity': 1, 'nt': [9, 19], 'qdim': 8, 'qvalues': [8, 2, 0, 8, 8, 8, -1, -1, -1, -1, 0, 0, 2, 0, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863864
      {'cdim': 8, 'counter': 14, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.8b', 'multiplicity': 1, 'nt': [18, 68], 'qdim': 8, 'qvalues': [8, -2, 0, 8, 8, 8, -1, -1, -1, -1, 0, 0, -2, 0, 0, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863865
      {'cdim': 8, 'counter': 15, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.8c', 'multiplicity': 2, 'nt': [24, 1330], 'qdim': 16, 'qvalues': [16, 4, 0, 16, -8, -8, -2, -2, 1, 1, 0, 0, 4, 0, 0, -2, -2, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863866
      {'cdim': 8, 'counter': 16, 'faithful': False, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.8d', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -4, 0, 16, -8, -8, -2, -2, 1, 1, 0, 0, -4, 0, 0, 2, 2, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863867
      {'cdim': 24, 'counter': 17, 'faithful': True, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.24a', 'multiplicity': 1, 'nt': [27, 542], 'qdim': 24, 'qvalues': [24, 6, 0, -3, 0, 0, 6, -3, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863868
      {'cdim': 24, 'counter': 18, 'faithful': True, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.24b', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 24, 'qvalues': [24, -6, 0, -3, 0, 0, 6, -3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
    • id: 15863869
      {'cdim': 48, 'counter': 19, 'faithful': True, 'group': '3888.el', 'group_order': 3888, 'image': None, 'label': '3888.el.48a', 'multiplicity': 1, 'nt': [54, 0], 'qdim': 48, 'qvalues': [48, 0, 0, -6, 0, 0, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • gps_char • Show schema
    • id: 35859053
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': None, 'kernel_order': 3888, 'label': '3888.el.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 35859064
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1944, 'label': '3888.el.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
    • id: 35859075
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1944, 'label': '3888.el.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 35859077
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': None, 'kernel_order': 1944, 'label': '3888.el.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
    • id: 35859078
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': None, 'kernel_order': 1296, 'label': '3888.el.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
    • id: 35859079
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': None, 'kernel_order': 1296, 'label': '3888.el.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
    • id: 35859080
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': None, 'kernel_order': 648, 'label': '3888.el.1f1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
    • id: 35859081
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': None, 'kernel_order': 648, 'label': '3888.el.1f2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
    • id: 35859082
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': None, 'kernel_order': 648, 'label': '3888.el.1g1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
    • id: 35859054
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': None, 'kernel_order': 648, 'label': '3888.el.1g2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
    • id: 35859055
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': None, 'kernel_order': 648, 'label': '3888.el.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
    • id: 35859056
      {'center': None, 'center_index': 1, 'center_order': 3888, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': None, 'kernel_order': 648, 'label': '3888.el.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
    • id: 35859057
      {'center': None, 'center_index': 4, 'center_order': 972, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': None, 'kernel_order': 486, 'label': '3888.el.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859058
      {'center': None, 'center_index': 8, 'center_order': 486, 'counter': 14, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': None, 'kernel_order': 243, 'label': '3888.el.2b1', 'nt': [8, 8], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]]]}
    • id: 35859059
      {'center': None, 'center_index': 8, 'center_order': 486, 'counter': 15, 'cyclotomic_n': 8, 'dim': 2, 'faithful': False, 'field': [2, 0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '16.8', 'image_order': 16, 'indicator': 0, 'kernel': None, 'kernel_order': 243, 'label': '3888.el.2b2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, 3]], [[1, 1], [1, 3]]]}
    • id: 35859060
      {'center': None, 'center_index': 4, 'center_order': 972, 'counter': 16, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': None, 'kernel_order': 162, 'label': '3888.el.2c1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859061
      {'center': None, 'center_index': 4, 'center_order': 972, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': None, 'kernel_order': 162, 'label': '3888.el.2c2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859062
      {'center': None, 'center_index': 8, 'center_order': 486, 'counter': 18, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [4, 0, -2, 0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '48.26', 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 81, 'label': '3888.el.2d1', 'nt': [24, 41], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 4]], [[2, 8]], [[2, 0]], [[2, 0]], [[2, 8]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3], [1, 5], [-1, 7]], [[1, 1], [-1, 7]], [[-1, 3], [-1, 5], [1, 7]], [[-1, 1], [1, 7]]]}
    • id: 35859063
      {'center': None, 'center_index': 8, 'center_order': 486, 'counter': 19, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [4, 0, -2, 0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '48.26', 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 81, 'label': '3888.el.2d2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 8]], [[-2, 4]], [[2, 0]], [[2, 0]], [[-2, 4]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 7]], [[1, 3], [1, 5], [-1, 7]], [[-1, 1], [1, 7]], [[-1, 3], [-1, 5], [1, 7]]]}
    • id: 35859065
      {'center': None, 'center_index': 8, 'center_order': 486, 'counter': 20, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [4, 0, -2, 0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '48.26', 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 81, 'label': '3888.el.2d3', 'nt': [24, 41], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 4]], [[2, 8]], [[2, 0]], [[2, 0]], [[2, 8]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 8]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 3], [1, 5]], [[1, 1], [-1, 3], [-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3], [-1, 5], [1, 7]], [[-1, 1], [1, 7]], [[1, 3], [1, 5], [-1, 7]], [[1, 1], [-1, 7]]]}
    • id: 35859066
      {'center': None, 'center_index': 8, 'center_order': 486, 'counter': 21, 'cyclotomic_n': 24, 'dim': 2, 'faithful': False, 'field': [4, 0, -2, 0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '48.26', 'image_order': 48, 'indicator': 0, 'kernel': None, 'kernel_order': 81, 'label': '3888.el.2d4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 8]], [[-2, 4]], [[2, 0]], [[2, 0]], [[-2, 4]], [[2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 8]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-1, 3], [-1, 5]], [[-1, 1], [1, 3], [1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [1, 7]], [[-1, 3], [-1, 5], [1, 7]], [[1, 1], [-1, 7]], [[1, 3], [1, 5], [-1, 7]]]}
    • id: 35859067
      {'center': None, 'center_index': 144, 'center_order': 27, 'counter': 22, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '3888.el.8a', 'nt': [9, 19], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859068
      {'center': None, 'center_index': 144, 'center_order': 27, 'counter': 23, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '144.182', 'image_order': 144, 'indicator': 1, 'kernel': None, 'kernel_order': 27, 'label': '3888.el.8b', 'nt': [18, 68], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859069
      {'center': None, 'center_index': 144, 'center_order': 27, 'counter': 24, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '432.737', 'image_order': 432, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '3888.el.8c1', 'nt': [24, 1330], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[8, -1]], [[8, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859070
      {'center': None, 'center_index': 144, 'center_order': 27, 'counter': 25, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '432.737', 'image_order': 432, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '3888.el.8c2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[2, 0]], [[0, 0]], [[8, 0]], [[8, 1]], [[8, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859071
      {'center': None, 'center_index': 144, 'center_order': 27, 'counter': 26, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '432.737', 'image_order': 432, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '3888.el.8d1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[8, -1]], [[8, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859072
      {'center': None, 'center_index': 144, 'center_order': 27, 'counter': 27, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '432.737', 'image_order': 432, 'indicator': 0, 'kernel': None, 'kernel_order': 9, 'label': '3888.el.8d2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-2, 0]], [[0, 0]], [[8, 0]], [[8, 1]], [[8, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859073
      {'center': None, 'center_index': 3888, 'center_order': 1, 'counter': 28, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '3888.el', 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3888.el.24a', 'nt': [27, 542], 'q_character': None, 'values': [[[24, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859074
      {'center': None, 'center_index': 3888, 'center_order': 1, 'counter': 29, 'cyclotomic_n': 1, 'dim': 24, 'faithful': True, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '3888.el', 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3888.el.24b', 'nt': [54, 0], 'q_character': None, 'values': [[[24, 0]], [[-6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
    • id: 35859076
      {'center': None, 'center_index': 3888, 'center_order': 1, 'counter': 30, 'cyclotomic_n': 1, 'dim': 48, 'faithful': True, 'field': [0, 1], 'group': '3888.el', 'group_counter': 116, 'group_order': 3888, 'image': None, 'image_isoclass': '3888.el', 'image_order': 3888, 'indicator': 1, 'kernel': None, 'kernel_order': 1, 'label': '3888.el.48a', 'nt': [54, 0], 'q_character': None, 'values': [[[48, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • gps_subgroup_search • Show schema
    Showing the first 100 of 155 matching records in this table.
    • id: 204460492
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 3888, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '3888.el.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3888.el', 'subgroup_hash': 401516246772182357, 'subgroup_order': 3888, 'subgroup_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'supersolvable': False, 'sylow': 0}
    • id: 204460559
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1944, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2314', 'subgroup_hash': 2314, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
    • id: 204460570
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1944, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2330', 'subgroup_hash': 2330, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^3:\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 204460581
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1944, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.2298', 'subgroup_hash': 2298, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_{24}', 'supersolvable': False, 'sylow': 0}
    • id: 204460592
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3521', 'subgroup_hash': 3521, 'subgroup_order': 1296, 'subgroup_tex': 'C_3^4:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
    • id: 204460603
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 972, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 204460614
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.427', 'subgroup_hash': 427, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460625
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 486, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '972.406', 'subgroup_hash': 406, 'subgroup_order': 972, 'subgroup_tex': 'C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 204460636
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.725', 'subgroup_hash': 725, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 204460493
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.730', 'subgroup_hash': 730, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 204460504
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.711', 'subgroup_hash': 711, 'subgroup_order': 648, 'subgroup_tex': 'C_3^2:F_9', 'supersolvable': False, 'sylow': 0}
    • id: 204460515
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 486, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.146', 'subgroup_hash': 146, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460526
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 243, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.102', 'subgroup_hash': 102, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460537
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.9.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.737', 'subgroup_hash': 737, 'subgroup_order': 432, 'subgroup_tex': 'F_9:C_6', 'supersolvable': False, 'sylow': 0}
    • id: 204460548
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 324, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 204460555
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.116', 'subgroup_hash': 116, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460556
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.169', 'subgroup_hash': 169, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460557
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 162, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '324.164', 'subgroup_hash': 164, 'subgroup_order': 324, 'subgroup_tex': 'C_3^4:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 204460558
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 243, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '3888.el.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.37', 'subgroup_hash': 37, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 3}
    • id: 204460560
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.157', 'subgroup_hash': 157, 'subgroup_order': 216, 'subgroup_tex': 'S_3^2:C_6', 'supersolvable': False, 'sylow': 0}
    • id: 204460561
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.160', 'subgroup_hash': 160, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': False, 'sylow': 0}
    • id: 204460562
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.154', 'subgroup_hash': 154, 'subgroup_order': 216, 'subgroup_tex': 'C_3\\times F_9', 'supersolvable': False, 'sylow': 0}
    • id: 204460563
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 162, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.54', 'subgroup_hash': 54, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460564
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460565
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460566
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.34', 'subgroup_hash': 34, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460567
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
    • id: 204460568
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.40', 'subgroup_hash': 40, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460569
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.182', 'subgroup_hash': 182, 'subgroup_order': 144, 'subgroup_tex': 'F_9:C_2', 'supersolvable': False, 'sylow': 0}
    • id: 204460571
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.182', 'subgroup_hash': 182, 'subgroup_order': 144, 'subgroup_tex': 'F_9:C_2', 'supersolvable': False, 'sylow': 0}
    • id: 204460572
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460573
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.25', 'subgroup_hash': 25, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460574
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460575
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460576
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 204460577
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.36', 'subgroup_hash': 36, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 204460578
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 81, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times \\SD_{16}', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'D2', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
    • id: 204460579
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460580
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460582
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
    • id: 204460583
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.40', 'subgroup_hash': 40, 'subgroup_order': 72, 'subgroup_tex': '\\SOPlus(4,2)', 'supersolvable': False, 'sylow': 0}
    • id: 204460584
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.41', 'subgroup_hash': 41, 'subgroup_order': 72, 'subgroup_tex': '\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 204460585
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
    • id: 204460586
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.41', 'subgroup_hash': 41, 'subgroup_order': 72, 'subgroup_tex': '\\PSU(3,2)', 'supersolvable': False, 'sylow': 0}
    • id: 204460587
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.54.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
    • id: 204460588
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.39', 'subgroup_hash': 39, 'subgroup_order': 72, 'subgroup_tex': 'F_9', 'supersolvable': False, 'sylow': 0}
    • id: 204460589
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460590
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460591
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460593
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460594
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460595
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460596
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460597
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460598
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460599
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460600
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.5', 'subgroup_hash': 5, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460601
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460602
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460604
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460605
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460606
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.26', 'subgroup_hash': 26, 'subgroup_order': 48, 'subgroup_tex': 'C_3\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
    • id: 204460607
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460608
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460609
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460610
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460611
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 204460612
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460613
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 204460615
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 204460616
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 204460617
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 204460618
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 204460619
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.108.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.9', 'subgroup_hash': 9, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 204460620
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 27, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '3888.el.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.182', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 182, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_9:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 204460621
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460622
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460623
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 204460624
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460626
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 204460627
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460628
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 204460629
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 204460630
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
    • id: 204460631
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
    • id: 204460632
      {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3888.el.162.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
    • id: 204460633
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460634
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460635
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
    • id: 204460637
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460638
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460639
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460640
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460641
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460642
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460643
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.i1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.i1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460644
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 1, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460645
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460646
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
    • id: 204460494
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3888.el', 'ambient_counter': 116, 'ambient_order': 3888, 'ambient_tex': 'C_3^4:(C_3\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3888.el.216.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 155 matching records in this table.
    • id: 204460492
      {'ambient': '3888.el', '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': '3888.a1.a1', 'complements': ['3888.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '9.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8342, 2975, 8750, 2952, 1867, 4685, 1923, 4685], 'generators': [3, 1296, 3864, 768, 6, 1884, 3024, 2304, 2], 'label': '3888.el.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.el'}
    • id: 204460493
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 1, 'centralizer': '3888.a1.a1', 'complements': ['648.d1.a1', '648.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '54.c1.a1', '54.e1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8971, 3314, 8588, 3248, 2108, 8484, 2187, 8484], 'generators': [9, 1728, 1872, 1884, 1296, 120, 3792], 'label': '3888.el.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.el'}
    • id: 204460494
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.n1.a1', '72.o1.a1'], 'contains': ['432.c2.a1', '648.h1.a1', '648.i1.a1', '648.j1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [6632, -1, 6593, -1, 3441, -1, 3305, -1], 'generators': [1704, 3504, 3024], 'label': '3888.el.216.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.m1.a1', 'old_label': '216.m1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 204460495
      {'ambient': '3888.el', 'aut_centralizer_order': 2, 'aut_label': '216.m2', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.n1.a1', '72.o1.a1', '108.b1.a1'], 'contains': ['432.c1.a1', '648.h1.a1', '648.i1.a1', '648.j1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6385, -1, 4850, -1, 3643, -1, 3505, -1], 'generators': [1272, 48, 1296], 'label': '3888.el.216.m2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.b1.a1', 'old_label': '216.m2.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m2.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 204460496
      {'ambient': '3888.el', 'aut_centralizer_order': 2, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '108.17', 'aut_weyl_index': 72, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '72.n1.a1', '72.o1.a1', '108.f1.a1'], 'contains': ['432.d1.a1', '648.h1.a1', '648.i1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5653, -1, 3308, -1, 5504, -1, 5640, -1], 'generators': [3000, 912, 432], 'label': '3888.el.216.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '216.n1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 204460497
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '108.17', 'aut_weyl_index': 72, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '72.m1.a1', '72.o1.a1'], 'contains': ['432.e1.a1', '648.h1.a1', '648.j1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [5849, -1, 3727, -1, 4031, -1, 3888, -1], 'generators': [3000, 2208, 432], 'label': '3888.el.216.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.k1.a1', 'old_label': '216.o1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 204460498
      {'ambient': '3888.el', 'aut_centralizer_order': 6, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1.a1', '72.o1.a1', '108.c1.a1', '108.g1.a1', '108.h1.a1'], 'contains': ['432.a1.a1', '648.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6099, -1, 4574, -1, 5301, -1, 5439, -1], 'generators': [3864, 432, 1296], 'label': '3888.el.216.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.p1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460499
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.n1.a1'], 'contains': ['432.g1.a1', '648.i1.a1', '648.j1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [7004, -1, 6955, -1, 2360, -1, 2238, -1], 'generators': [3864, 1344, 2304], 'label': '3888.el.216.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.q1.a1', 'old_label': '216.q1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 204460500
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '36.9', 'aut_weyl_index': 216, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.n1.a1'], 'contains': ['432.h2.a1', '648.i1.a1', '648.j1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [7156, -1, 7105, -1, 2563, -1, 2438, -1], 'generators': [3864, 3504, 2304], 'label': '3888.el.216.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.r1.a1', 'old_label': '216.r1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
    • id: 204460501
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '216.r2', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '72.40', 'aut_weyl_index': 108, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.n1.a1', '108.d1.a1'], 'contains': ['432.h1.a1', '648.i1.a1', '648.j1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6785, -1, 6806, -1, 2968, -1, 2839, -1], 'generators': [3864, 912, 2304], 'label': '3888.el.216.r2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.d1.a1', 'old_label': '216.r2.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r2.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
    • id: 204460502
      {'ambient': '3888.el', 'aut_centralizer_order': 2, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1.a1', '108.e1.a1', '108.i1.a1', '108.j1.a1'], 'contains': ['432.i1.a1', '648.i1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8564, -1, 7319, -1, 2765, -1, 2638, -1], 'generators': [3864, 48, 1872], 'label': '3888.el.216.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '216.s1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460503
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '108.k1.a1'], 'contains': ['432.j1.a1', '648.j1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7527, -1, 7682, -1, 1867, -1, 1752, -1], 'generators': [3864, 3072, 2304], 'label': '3888.el.216.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1.a1', 'old_label': '216.t1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
    • id: 204460504
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 1, 'centralizer': '3888.a1.a1', 'complements': ['648.d1.a1', '648.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '54.d1.a1', '54.f1.a1', '54.g1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9553, 5146, 9654, 1269, 907, 5207, 935, 5207], 'generators': [6, 1728, 144, 12, 1296, 24, 480], 'label': '3888.el.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.el'}
    • id: 204460505
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '216.t2', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '72.41', 'aut_weyl_index': 108, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '108.l1.a1'], 'contains': ['432.j2.a1', '648.j1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [7309, -1, 7468, -1, 2070, -1, 1952, -1], 'generators': [3864, 1776, 2304], 'label': '3888.el.216.t2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.l1.a1', 'old_label': '216.t2.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t2.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
    • id: 204460506
      {'ambient': '3888.el', 'aut_centralizer_order': 12, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 972, 'centralizer': '648.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1', '81.a1.a1'], 'contains': ['486.a1.a1', '486.b1.a1', '486.c1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8978, -1, 9261, -1, 829, -1, 599, -1], 'generators': [3, 3798], 'label': '3888.el.243.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '243.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
    • id: 204460507
      {'ambient': '3888.el', 'aut_centralizer_order': 12, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '162.a1.a1'], 'contains': ['648.b1.a1', '648.g1.a1', '972.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [6130, -1, 4700, -1, 4285, -1, 4139, -1], 'generators': [3, 3864, 962], 'label': '3888.el.324.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460508
      {'ambient': '3888.el', 'aut_centralizer_order': 12, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.a1', '108.c1.a1', '108.f1.a1'], 'contains': ['648.a1.a1', '648.e1.a1', '648.h1.a1', '972.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4485, -1, 3153, -1, 5988, -1, 6414, -1], 'generators': [3, 3864, 432], 'label': '3888.el.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '324.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 204460509
      {'ambient': '3888.el', 'aut_centralizer_order': 4, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.d1.a1', '108.e1.a1', '108.f1.a1'], 'contains': ['648.c1.a1', '648.f1.a1', '648.i1.a1', '972.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [5446, -1, 4933, -1, 4517, -1, 4368, -1], 'generators': [3, 3864, 48], 'label': '3888.el.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.c1.a1', 'old_label': '324.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 204460510
      {'ambient': '3888.el', 'aut_centralizer_order': 24, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '162.a1.a1', '162.b1.a1', '162.c1.a1'], 'contains': ['648.g1.a1', '972.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [7996, -1, 8368, -1, 1301, -1, 1109, -1], 'generators': [1884, 962, 3864], 'label': '3888.el.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '324.d1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460511
      {'ambient': '3888.el', 'aut_centralizer_order': 12, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '324.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '162.b1.a1'], 'contains': ['648.g1.a1', '972.c1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [7658, -1, 7799, -1, 1667, -1, 1554, -1], 'generators': [9, 1394, 120], 'label': '3888.el.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1.a1', 'old_label': '324.e1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460512
      {'ambient': '3888.el', 'aut_centralizer_order': 486, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '16.8', 'aut_weyl_index': 486, 'centralizer': '16.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.h1.a1', '144.i1.a1', '216.h1.a1', '216.p1.a1'], 'contains': ['1296.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1145, 8048, 1963, 8206, 7701, 3945, 7583, 3945], 'generators': [432, 1296], 'label': '3888.el.432.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['48.a1.a1', '144.a1.a1'], 'normal_contains': ['3888.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': '16.8', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
    • id: 204460513
      {'ambient': '3888.el', 'aut_centralizer_order': 54, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '216.a1.a1', '216.d1.a1', '216.l1.a1'], 'contains': ['1296.a1.a1', '1296.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2006, -1, 903, -1, 8000, -1, 8069, -1], 'generators': [3554, 432], 'label': '3888.el.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '432.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 204460514
      {'ambient': '3888.el', 'aut_centralizer_order': 162, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.f1.a1', '144.h1.a1', '216.e1.a1', '216.f1.a1', '216.m2.a1'], 'contains': ['1296.a1.a1', '1296.c1.a1', '1296.d1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3568, -1, 4308, -1, 4822, -1, 4425, -1], 'generators': [2640, 1296], 'label': '3888.el.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '432.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 204460515
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 1, 'centralizer': '3888.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.f1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5679, 7853, 5489, 8152, 4842, 3350, 4832, 3350], 'generators': [3864, 1296, 432, 2, 480, 2304], 'label': '3888.el.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.el'}
    • id: 204460516
      {'ambient': '3888.el', 'aut_centralizer_order': 81, 'aut_label': '432.c2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.f1.a1', '144.h1.a1', '216.m1.a1'], 'contains': ['1296.a1.a1', '1296.c1.a1', '1296.d1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4131, -1, 6014, -1, 4209, -1, 4064, -1], 'generators': [480, 3024], 'label': '3888.el.432.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '432.c2.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460517
      {'ambient': '3888.el', 'aut_centralizer_order': 162, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.e1.a1', '144.f1.a1', '144.h1.a1', '216.b1.a1', '216.k1.a1', '216.n1.a1'], 'contains': ['1296.a1.a1', '1296.c1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2553, -1, 2882, -1, 6928, -1, 6887, -1], 'generators': [480, 432], 'label': '3888.el.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '432.d1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 204460518
      {'ambient': '3888.el', 'aut_centralizer_order': 81, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '144.d1.a1', '144.g1.a1', '144.h1.a1', '216.o1.a1'], 'contains': ['1296.a1.a1', '1296.d1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2415, -1, 3584, -1, 6745, -1, 6707, -1], 'generators': [1776, 432], 'label': '3888.el.432.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '432.e1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
    • id: 204460519
      {'ambient': '3888.el', 'aut_centralizer_order': 54, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.c1.a1', '144.i1.a1', '216.c1.a1'], 'contains': ['1296.a1.a1', '1296.e1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [887, -1, 433, -1, 8722, -1, 8815, -1], 'generators': [2, 432], 'label': '3888.el.432.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.b1.a1', 'old_label': '432.f1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
    • id: 204460520
      {'ambient': '3888.el', 'aut_centralizer_order': 27, 'aut_label': '432.f2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '144.g1.a1', '144.i1.a1'], 'contains': ['1296.a1.a1', '1296.e1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [499, -1, 2097, -1, 9348, -1, 9554, -1], 'generators': [2, 3024], 'label': '3888.el.432.f2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.c1.a1', 'old_label': '432.f2.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f2.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
    • id: 204460521
      {'ambient': '3888.el', 'aut_centralizer_order': 27, 'aut_label': '432.f3', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '144.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '144.g1.a1', '144.i1.a1', '216.g1.a1'], 'contains': ['1296.a1.a1', '1296.e1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [335, -1, 1334, -1, 9166, -1, 9343, -1], 'generators': [2, 1296], 'label': '3888.el.432.f3.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '432.f3.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f3.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 204460522
      {'ambient': '3888.el', 'aut_centralizer_order': 81, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1944, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.f1.a1', '216.q1.a1'], 'contains': ['1296.c1.a1', '1296.d1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5008, -1, 6211, -1, 3158, -1, 3026, -1], 'generators': [1344, 2304], 'label': '3888.el.432.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '432.g1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460523
      {'ambient': '3888.el', 'aut_centralizer_order': 81, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 972, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.f1.a1', '216.i1.a1', '216.i1.a2', '216.r2.a1'], 'contains': ['1296.c1.a1', '1296.d1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4269, -1, 5879, -1, 4027, -1, 3884, -1], 'generators': [912, 2304], 'label': '3888.el.432.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '432.h1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 204460524
      {'ambient': '3888.el', 'aut_centralizer_order': 81, 'aut_label': '432.h2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.1', 'aut_weyl_index': 1944, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.f1.a1', '216.r1.a1'], 'contains': ['1296.c1.a1', '1296.d1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4870, -1, 6431, -1, 3501, -1, 3364, -1], 'generators': [3504, 2304], 'label': '3888.el.432.h2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '432.h2.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460525
      {'ambient': '3888.el', 'aut_centralizer_order': 162, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.8', 'aut_weyl_index': 486, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1.a1', '216.j1.a1', '216.s1.a1'], 'contains': ['1296.c1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4406, -1, 5744, -1, 3844, -1, 3703, -1], 'generators': [48, 1872], 'label': '3888.el.432.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '432.i1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.8'}
    • id: 204460526
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '648.555', 'aut_weyl_index': 12, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2501, -1, 2782, -1, 7837, -1, 7862, -1], 'generators': [3, 1296, 3216, 2, 2304, 1728], 'label': '3888.el.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
    • id: 204460527
      {'ambient': '3888.el', 'aut_centralizer_order': 81, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.8', 'aut_weyl_index': 486, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '216.t1.a1'], 'contains': ['1296.d1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6833, -1, 7529, -1, 2632, -1, 2506, -1], 'generators': [3072, 2304], 'label': '3888.el.432.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '432.j1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.1'}
    • id: 204460528
      {'ambient': '3888.el', 'aut_centralizer_order': 81, 'aut_label': '432.j2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.4', 'aut_weyl_index': 972, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '216.t2.a1'], 'contains': ['1296.d1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6377, -1, 7118, -1, 2815, -1, 2687, -1], 'generators': [1776, 2304], 'label': '3888.el.432.j2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '432.j2.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j2.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
    • id: 204460529
      {'ambient': '3888.el', 'aut_centralizer_order': 12, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 972, 'centralizer': '648.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.b1.a1', '162.a1.a1', '243.a1.a1'], 'contains': ['972.a1.a1', '972.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8369, -1, 8145, -1, 1745, -1, 1578, -1], 'generators': [3, 1884], 'label': '3888.el.486.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '486.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
    • id: 204460530
      {'ambient': '3888.el', 'aut_centralizer_order': 12, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '8.3', 'aut_weyl_index': 972, 'centralizer': '648.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1.a1', '54.e1.a1', '162.b1.a1', '243.a1.a1'], 'contains': ['972.b1.a1', '972.c1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8716, -1, 8840, -1, 1143, -1, 1197, -1], 'generators': [9, 1980], 'label': '3888.el.486.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '486.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
    • id: 204460531
      {'ambient': '3888.el', 'aut_centralizer_order': 48, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '54.f1.a1', '54.g1.a1', '162.c1.a1', '243.a1.a1'], 'contains': ['972.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [9514, -1, 9746, -1, 354, -1, 405, -1], 'generators': [6], 'label': '3888.el.486.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '486.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460532
      {'ambient': '3888.el', 'aut_centralizer_order': 108, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.e1.a1', '216.h1.a1', '324.b1.a1'], 'contains': ['1296.a1.a1', '1944.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1598, -1, 1939, -1, 7421, -1, 7215, -1], 'generators': [3, 432], 'label': '3888.el.648.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '648.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460533
      {'ambient': '3888.el', 'aut_centralizer_order': 36, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.d1.a1', '324.a1.a1'], 'contains': ['1296.b1.a1', '1944.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [2966, -1, 773, -1, 7100, -1, 7057, -1], 'generators': [3, 98], 'label': '3888.el.648.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '648.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 204460534
      {'ambient': '3888.el', 'aut_centralizer_order': 36, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '216.f1.a1', '216.i1.a1', '216.i1.a2', '216.j1.a1', '324.c1.a1'], 'contains': ['1296.c1.a1', '1944.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [3503, -1, 4816, -1, 5030, -1, 5032, -1], 'generators': [3, 48], 'label': '3888.el.648.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.f1.a1', 'old_label': '648.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460535
      {'ambient': '3888.el', 'aut_centralizer_order': 18, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.c1.a1', '216.g1.a1'], 'contains': ['1296.e1.a1', '1944.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [593, -1, 308, -1, 8923, -1, 9015, -1], 'generators': [3, 2], 'label': '3888.el.648.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '216.c1.a1', 'old_label': '648.d1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 204460536
      {'ambient': '3888.el', 'aut_centralizer_order': 108, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '72.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.d1.a1', '216.f1.a1', '216.g1.a1', '216.h1.a1', '216.k1.a1', '324.b1.a1'], 'contains': ['1296.a1.a1', '1944.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2759, -1, 1808, -1, 7260, -1, 7374, -1], 'generators': [3, 1296], 'label': '3888.el.648.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '648.e1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 204460537
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 27, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '27.a1.a1', '81.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8520, -1, 8989, -1, 1700, -1, 1785, -1], 'generators': [3, 432, 3864, 774, 1296, 2690, 1884], 'label': '3888.el.9.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460538
      {'ambient': '3888.el', 'aut_centralizer_order': 36, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '216.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '216.i1.a1', '216.i1.a2', '216.j1.a1', '216.k1.a1', '324.c1.a1'], 'contains': ['1296.c1.a1', '1944.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3823, -1, 5209, -1, 5190, -1, 5191, -1], 'generators': [3, 3216], 'label': '3888.el.648.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '648.f1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 204460539
      {'ambient': '3888.el', 'aut_centralizer_order': 48, 'aut_label': '648.g1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.l1.a1', '324.a1.a1', '324.d1.a1', '324.e1.a1'], 'contains': ['1296.b1.a1', '1944.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [7004, -1, 7460, -1, 3329, -1, 3195, -1], 'generators': [3864, 962], 'label': '3888.el.648.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '648.g1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 204460540
      {'ambient': '3888.el', 'aut_centralizer_order': 12, 'aut_label': '648.h1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.l1.a1', '216.m1.a1', '216.m2.a1', '216.n1.a1', '216.o1.a1', '216.p1.a1', '324.b1.a1'], 'contains': ['1296.a1.a1', '1944.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5666, -1, 3592, -1, 4651, -1, 4874, -1], 'generators': [3864, 432], 'label': '3888.el.648.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.a1.a1', 'old_label': '648.h1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.h1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 204460541
      {'ambient': '3888.el', 'aut_centralizer_order': 4, 'aut_label': '648.i1', 'aut_quo_index': None, 'aut_stab_index': 324, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.m1.a1', '216.m2.a1', '216.n1.a1', '216.q1.a1', '216.r1.a1', '216.r2.a1', '216.s1.a1', '324.c1.a1'], 'contains': ['1296.c1.a1', '1944.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 324, 'diagramx': [6510, -1, 6671, -1, 3672, -1, 3534, -1], 'generators': [3864, 48], 'label': '3888.el.648.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '324.c1.a1', 'old_label': '648.i1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 204460542
      {'ambient': '3888.el', 'aut_centralizer_order': 2, 'aut_label': '648.j1', 'aut_quo_index': None, 'aut_stab_index': 648, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1296, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.m1.a1', '216.m2.a1', '216.o1.a1', '216.q1.a1', '216.r1.a1', '216.r2.a1', '216.t1.a1', '216.t2.a1'], 'contains': ['1296.d1.a1', '1944.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 648, 'diagramx': [7244, -1, 7217, -1, 2986, -1, 2856, -1], 'generators': [3864, 1344], 'label': '3888.el.648.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '648.j1.a1', 'old_label': '648.j1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 204460543
      {'ambient': '3888.el', 'aut_centralizer_order': 24, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '324.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1.a1', '324.b1.a1', '324.c1.a1', '486.a1.a1'], 'contains': ['1944.a1.a1', '1944.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [6041, -1, 4235, -1, 4410, -1, 4245, -1], 'generators': [3, 3864], 'label': '3888.el.972.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.a1.a1', 'old_label': '972.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460544
      {'ambient': '3888.el', 'aut_centralizer_order': 48, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '162.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '108.i1.a1', '108.k1.a1', '324.d1.a1', '486.a1.a1', '486.b1.a1', '486.c1.a1'], 'contains': ['1944.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8621, -1, 8588, -1, 949, -1, 887, -1], 'generators': [1884], 'label': '3888.el.972.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '972.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460545
      {'ambient': '3888.el', 'aut_centralizer_order': 24, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': 162, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '324.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.h1.a1', '108.j1.a1', '108.l1.a1', '324.e1.a1', '486.b1.a1'], 'contains': ['1944.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 162, 'diagramx': [7827, -1, 7976, -1, 1596, -1, 1483, -1], 'generators': [9], 'label': '3888.el.972.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '162.b1.a1', 'old_label': '972.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460546
      {'ambient': '3888.el', 'aut_centralizer_order': 972, 'aut_label': '1296.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '432.b1.a1', '432.c1.a1', '432.c2.a1', '432.d1.a1', '432.e1.a1', '432.f1.a1', '432.f2.a1', '432.f3.a1', '648.a1.a1', '648.e1.a1', '648.h1.a1'], 'contains': ['3888.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2529, -1, 2082, -1, 7260, -1, 7215, -1], 'generators': [432], 'label': '3888.el.1296.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '1296.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460547
      {'ambient': '3888.el', 'aut_centralizer_order': 432, 'aut_label': '1296.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.b1.a1', '648.b1.a1', '648.g1.a1'], 'contains': ['3888.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2966, -1, 830, -1, 6939, -1, 6899, -1], 'generators': [2690], 'label': '3888.el.1296.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '1296.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 204460548
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '12.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 1, 'centralizer': '3888.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '108.g1.a1', '108.i1.a1', '108.k1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9095, 5049, 8583, 5001, 2108, 5729, 2168, 5729], 'generators': [1884, 1296, 3024, 3864, 624, 144], 'label': '3888.el.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.c1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.el'}
    • id: 204460549
      {'ambient': '3888.el', 'aut_centralizer_order': 324, 'aut_label': '1296.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '432.c2.a1', '432.d1.a1', '432.g1.a1', '432.h1.a1', '432.h2.a1', '432.i1.a1', '648.c1.a1', '648.f1.a1', '648.i1.a1'], 'contains': ['3888.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4205, -1, 5528, -1, 4209, -1, 4064, -1], 'generators': [48], 'label': '3888.el.1296.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '1296.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460550
      {'ambient': '3888.el', 'aut_centralizer_order': 162, 'aut_label': '1296.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.c1.a1', '432.c2.a1', '432.e1.a1', '432.g1.a1', '432.h1.a1', '432.h2.a1', '432.j1.a1', '432.j2.a1', '648.j1.a1'], 'contains': ['3888.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [4747, -1, 6114, -1, 3844, -1, 3703, -1], 'generators': [1344], 'label': '3888.el.1296.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '1296.d1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 204460551
      {'ambient': '3888.el', 'aut_centralizer_order': 54, 'aut_label': '1296.e1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3888, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['432.f1.a1', '432.f2.a1', '432.f3.a1', '648.d1.a1'], 'contains': ['3888.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [563, -1, 557, -1, 8923, -1, 9015, -1], 'generators': [2], 'label': '3888.el.1296.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '72.e1.a1', 'old_label': '1296.e1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 204460552
      {'ambient': '3888.el', 'aut_centralizer_order': 216, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7776, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.a1.a1', '648.b1.a1', '648.c1.a1', '648.d1.a1', '648.e1.a1', '648.f1.a1', '972.a1.a1'], 'contains': ['3888.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3058, -1, 1944, -1, 7100, -1, 7057, -1], 'generators': [3], 'label': '3888.el.1944.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '1944.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 204460553
      {'ambient': '3888.el', 'aut_centralizer_order': 96, 'aut_label': '1944.b1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 7776, 'centralizer': '81.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['648.g1.a1', '648.h1.a1', '648.i1.a1', '648.j1.a1', '972.a1.a1', '972.b1.a1', '972.c1.a1'], 'contains': ['3888.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [7052, -1, 7335, -1, 3501, -1, 3364, -1], 'generators': [3864], 'label': '3888.el.1944.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1.a1', 'old_label': '1944.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 204460554
      {'ambient': '3888.el', 'aut_centralizer_order': None, 'aut_label': '3888.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1296.a1.a1', '1296.b1.a1', '1296.c1.a1', '1296.d1.a1', '1296.e1.a1', '1944.a1.a1', '1944.b1.a1'], 'contains': [], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3058, 8048, 2082, 8206, 6939, 3945, 6899, 3945], 'generators': [], 'label': '3888.el.3888.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '3888.a1.a1', 'normal_contained_in': ['432.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '3888.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 204460555
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '648.555', 'aut_weyl_index': 12, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.f1.a1', '36.a1.a1', '36.b1.a1', '36.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4140, -1, 1752, -1, 6202, -1, 6245, -1], 'generators': [3, 1296, 432, 3864, 2, 480], 'label': '3888.el.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '12.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
    • id: 204460556
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3888.bu', 'aut_weyl_index': 2, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '36.c1.a1', '36.d1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5406, -1, 5205, -1, 4533, -1, 4526, -1], 'generators': [3, 1296, 432, 3864, 1344, 576], 'label': '3888.el.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1944.2314'}
    • id: 204460557
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3888.ee', 'aut_weyl_index': 2, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1'], 'contains': ['24.a1.a1', '108.h1.a1', '108.j1.a1', '108.l1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8090, -1, 7869, -1, 3775, -1, 3811, -1], 'generators': [9, 1296, 1728, 120, 1344, 1440], 'label': '3888.el.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.d1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1944.2330'}
    • id: 204460558
      {'ambient': '3888.el', 'aut_centralizer_order': 9, 'aut_label': '16.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 9, 'centralizer': '432.a1.a1', 'complements': ['243.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2581, 8080, 3031, 8276, 8410, 3350, 8428, 3350], 'generators': [2, 1344, 2304], 'label': '3888.el.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1'], 'normal_contains': ['48.a1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': '16.8', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.737'}
    • id: 204460559
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 1, 'centralizer': '3888.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '6.a1.a1', '18.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7858, 1466, 8038, 7540, 2957, 3350, 3067, 3350], 'generators': [3, 768, 144, 1884, 3864, 1296, 3024, 2], 'label': '3888.el.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.el'}
    • id: 204460560
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 27, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.e1.a1', '54.a1.a1', '162.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7681, -1, 7807, -1, 3231, -1, 3274, -1], 'generators': [3, 1296, 3024, 1884, 2690, 3864], 'label': '3888.el.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460561
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 27, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.f1.a1', '54.c1.a1', '162.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8186, -1, 8489, -1, 2560, -1, 2781, -1], 'generators': [9, 1296, 432, 684, 2690, 120], 'label': '3888.el.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460562
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 27, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '54.d1.a1', '162.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9119, -1, 9497, -1, 1377, -1, 1648, -1], 'generators': [6, 1296, 432, 2690, 12, 24], 'label': '3888.el.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460563
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 1, 'centralizer': '3888.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.c1.a1', '12.d1.a1'], 'contains': ['48.a1.a1', '72.m1.a1', '72.n1.a1', '72.o1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6693, 6362, 5722, 6384, 4176, 5294, 4119, 5294], 'generators': [3864, 1296, 1344, 2304, 432], 'label': '3888.el.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.el'}
    • id: 204460564
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '216.162', 'aut_weyl_index': 36, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1636, -1, 1347, -1, 8069, -1, 8091, -1], 'generators': [3, 1296, 2, 1344, 432], 'label': '3888.el.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '24.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
    • id: 204460565
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '648.555', 'aut_weyl_index': 12, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1'], 'contains': ['48.b1.a1', '72.c1.a1', '72.f1.a1', '72.i1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2454, -1, 1752, -1, 7606, -1, 7633, -1], 'generators': [3, 1296, 2306, 432, 1920], 'label': '3888.el.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
    • id: 204460566
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '324.121', 'aut_weyl_index': 24, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1'], 'contains': ['48.c1.a1', '72.e1.a1', '72.g1.a1', '72.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [853, -1, 2183, -1, 9190, -1, 9200, -1], 'generators': [3, 1296, 2, 432, 3216], 'label': '3888.el.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '162.34'}
    • id: 204460567
      {'ambient': '3888.el', 'aut_centralizer_order': 9, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 36, 'centralizer': '432.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '72.b1.a1', '72.d1.a1', '72.h1.a1', '72.i1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3398, -1, 4955, -1, 5012, -1, 5061, -1], 'generators': [3, 1296, 2304, 432, 3216], 'label': '3888.el.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.e1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '108.25'}
    • id: 204460568
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '648.555', 'aut_weyl_index': 12, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1'], 'contains': ['48.b1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '72.o1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4851, -1, 2648, -1, 6202, -1, 6245, -1], 'generators': [3864, 1296, 2, 480, 432], 'label': '3888.el.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '24.f1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
    • id: 204460569
      {'ambient': '3888.el', 'aut_centralizer_order': 6, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '9.a1.a1'], 'contains': ['54.a1.a1', '54.c1.a1', '54.d1.a1', '243.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8582, -1, 9043, -1, 1674, -1, 1355, -1], 'generators': [3, 1296, 432, 774, 1884, 3864], 'label': '3888.el.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460570
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 1, 'centralizer': '3888.a1.a1', 'complements': ['1944.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.c1.a1', '6.b1.a1', '18.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8168, 4465, 8400, 4300, 2502, 6033, 2660, 6033], 'generators': [9, 768, 2304, 1884, 120, 1296, 3024, 2], 'label': '3888.el.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.el'}
    • id: 204460571
      {'ambient': '3888.el', 'aut_centralizer_order': 2, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['54.b1.a1', '54.e1.a1', '54.f1.a1', '243.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': '27T542', 'count': 27, 'diagramx': [9598, -1, 9368, -1, 419, -1, 500, -1], 'generators': [3, 1872, 1920, 6, 1884, 3864], 'label': '3888.el.27.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '27.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460572
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.186', 'aut_weyl_index': 54, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.a1.a1'], 'contains': ['72.c1.a1', '72.l1.a1', '108.a1.a1', '108.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4683, -1, 2996, -1, 5883, -1, 5908, -1], 'generators': [3, 1296, 3864, 2690, 3024], 'label': '3888.el.36.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.40'}
    • id: 204460573
      {'ambient': '3888.el', 'aut_centralizer_order': 2, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '108.17', 'aut_weyl_index': 72, 'centralizer': '1944.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1'], 'contains': ['72.a1.a1', '72.f1.a1', '72.j1.a1', '108.a1.a1', '108.f1.a1'], 'core': '3888.a1.a1', 'coset_action_label': '36T4958', 'count': 36, 'diagramx': [3738, -1, 1384, -1, 6652, -1, 7002, -1], 'generators': [3, 432, 3000, 2, 480], 'label': '3888.el.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '36.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '54.5'}
    • id: 204460574
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '216.162', 'aut_weyl_index': 36, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1'], 'contains': ['72.b1.a1', '72.h1.a1', '72.n1.a1', '108.b1.a1', '108.d1.a1', '108.e1.a1', '108.f1.a1'], 'core': '3888.a1.a1', 'coset_action_label': '36T4854', 'count': 36, 'diagramx': [5366, -1, 5674, -1, 4533, -1, 4526, -1], 'generators': [3, 432, 3000, 48, 3168], 'label': '3888.el.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '36.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
    • id: 204460575
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '648.555', 'aut_weyl_index': 12, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1'], 'contains': ['72.d1.a1', '72.i1.a1', '72.o1.a1', '108.b1.a1', '108.c1.a1', '108.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4289, -1, 3385, -1, 5484, -1, 5532, -1], 'generators': [3, 1296, 3864, 1344, 432], 'label': '3888.el.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '36.d1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '324.116'}
    • id: 204460576
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 27, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '18.a1.a1', '18.b1.a1', '18.c1.a1'], 'contains': ['72.l1.a1', '108.g1.a1', '324.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7575, -1, 8232, -1, 2835, -1, 3045, -1], 'generators': [1884, 1296, 2690, 3864, 3024], 'label': '3888.el.36.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460577
      {'ambient': '3888.el', 'aut_centralizer_order': 3, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '144.187', 'aut_weyl_index': 54, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '18.b1.a1'], 'contains': ['72.l1.a1', '108.h1.a1', '324.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7244, -1, 7595, -1, 3699, -1, 3648, -1], 'generators': [9, 1296, 2690, 120, 432], 'label': '3888.el.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1.a1', 'old_label': '36.f1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.41'}
    • id: 204460578
      {'ambient': '3888.el', 'aut_centralizer_order': 81, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.120', 'aut_weyl_index': 81, 'centralizer': '48.a1.a1', 'complements': ['81.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.e1.a1'], 'contains': ['144.d1.a1', '144.f1.a1', '144.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3180, 7561, 5116, 7680, 3940, 4539, 4014, 4539], 'generators': [1344, 2304, 432, 1296], 'label': '3888.el.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': '48.26', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '48.26'}
    • id: 204460579
      {'ambient': '3888.el', 'aut_centralizer_order': 9, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.162', 'aut_weyl_index': 36, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.c1.a1', '24.f1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.h1.a1', '144.i1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1762, -1, 1770, -1, 8800, -1, 8815, -1], 'generators': [2, 1344, 1296], 'label': '3888.el.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
    • id: 204460580
      {'ambient': '3888.el', 'aut_centralizer_order': 9, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '108.39', 'aut_weyl_index': 72, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.d1.a1'], 'contains': ['144.e1.a1', '144.g1.a1', '144.h1.a1', '144.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [853, -1, 2674, -1, 9580, -1, 9808, -1], 'generators': [2306, 1344, 1296], 'label': '3888.el.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '54.12'}
    • id: 204460581
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '7776.cw', 'aut_weyl_index': 1, 'centralizer': '3888.a1.a1', 'complements': ['1944.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.a1', '18.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9045, 6978, 9329, 1585, 1669, 885, 1727, 885], 'generators': [6, 2496, 2304, 2, 24, 1296, 3024, 12], 'label': '3888.el.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '3888.el'}
    • id: 204460582
      {'ambient': '3888.el', 'aut_centralizer_order': 6, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '18.a1.a1', '27.a1.a1'], 'contains': ['108.c1.a1', '108.g1.a1', '486.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7965, -1, 7424, -1, 3224, -1, 2660, -1], 'generators': [3, 1296, 1884, 3864, 3024], 'label': '3888.el.54.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460583
      {'ambient': '3888.el', 'aut_centralizer_order': 2, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '27.b1.a1'], 'contains': ['108.e1.a1', '108.i1.a1', '486.a1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9171, -1, 8132, -1, 1745, -1, 1721, -1], 'generators': [3, 144, 1884, 3864, 624], 'label': '3888.el.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460584
      {'ambient': '3888.el', 'aut_centralizer_order': 6, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '18.b1.a1', '27.a1.a1'], 'contains': ['108.g1.a1', '108.h1.a1', '486.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8434, -1, 8485, -1, 2026, -1, 2300, -1], 'generators': [9, 1296, 684, 120, 3024], 'label': '3888.el.54.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460585
      {'ambient': '3888.el', 'aut_centralizer_order': 6, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '1296.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '18.c1.a1', '27.a1.a1'], 'contains': ['108.g1.a1', '486.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8983, -1, 9597, -1, 1018, -1, 786, -1], 'generators': [6, 1296, 12, 24, 1728], 'label': '3888.el.54.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460586
      {'ambient': '3888.el', 'aut_centralizer_order': 2, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '27.b1.a1'], 'contains': ['108.i1.a1', '108.j1.a1', '486.b1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9509, -1, 8926, -1, 608, -1, 1142, -1], 'generators': [9, 1872, 1884, 120, 3792], 'label': '3888.el.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.e1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460587
      {'ambient': '3888.el', 'aut_centralizer_order': 2, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '27.b1.a1'], 'contains': ['108.i1.a1', '486.c1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [9717, -1, 9784, -1, 221, -1, 218, -1], 'generators': [6, 144, 12, 24, 768], 'label': '3888.el.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.b1.a1', 'old_label': '54.f1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.a1', 'subgroup_fusion': None, 'weyl_group': '144.182'}
    • id: 204460588
      {'ambient': '3888.el', 'aut_centralizer_order': 1, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '144.182', 'aut_weyl_index': 54, 'centralizer': '3888.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['108.k1.a1', '486.c1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9902, -1, 9903, -1, 60, -1, 59, -1], 'generators': [6, 1440, 12, 24, 1200], 'label': '3888.el.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.g1.a1', 'old_label': '54.g1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.39'}
    • id: 204460589
      {'ambient': '3888.el', 'aut_centralizer_order': 6, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '36.10', 'aut_weyl_index': 216, 'centralizer': '648.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.b1.a1'], 'contains': ['144.b1.a1', '216.a1.a1', '216.b1.a1', '216.c1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [1871, -1, 427, -1, 8370, -1, 8390, -1], 'generators': [3, 2, 48, 432], 'label': '3888.el.72.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.b1.a1', 'old_label': '72.a1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
    • id: 204460590
      {'ambient': '3888.el', 'aut_centralizer_order': 9, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 324, 'centralizer': '432.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.c1.a1'], 'contains': ['144.f1.a1', '216.b1.a1', '216.e1.a1', '216.i1.a1', '216.i1.a2', '216.j1.a1'], 'core': '3888.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3703, -1, 5214, -1, 5012, -1, 4526, -1], 'generators': [3, 2736, 432, 3216], 'label': '3888.el.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.c1.a1', 'old_label': '72.b1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 204460591
      {'ambient': '3888.el', 'aut_centralizer_order': 9, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 108, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '36.a1.a1'], 'contains': ['144.a1.a1', '216.a1.a1', '216.d1.a1', '216.h1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1512, -1, 1294, -1, 7980, -1, 8005, -1], 'generators': [3, 2690, 432, 1296], 'label': '3888.el.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '72.c1.a1', 'projective_image': '3888.el', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}