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  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [18, 36, 6, 12], 'aut_gens': [[169896969349937930797062205829531323841525, 84784991226554171514348914420873952985650, 74452114787817178376881809503970785874725], [159560035666965331274704319481286652239175, 319408233369570310815011922557168289519626, 84495725629726107028088583800838874074266], [297536042470462834524212871070926412175520, 138281561615703296522367465274337540959199, 148313517795438272083301618279468979376802], [371991433716561424792678435980122264813371, 10335041048563940545105241733913767479067, 10335303969411527833722934462496238223319], [297834271767268142142001425397419943900556, 84492203006703147534562044359838380682506, 191473672357929942798442684437048620065895]], 'aut_group': None, 'aut_hash': 3757498835710374883, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 102036672, 'aut_permdeg': 3024, 'aut_perms': 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'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': None, 'autcentquo_hash': 3757498835710374883, 'autcentquo_nilpotent': False, 'autcentquo_order': 102036672, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^6.C_3^4.C_6^3.C_2^3', 'cc_stats': [[1, 1, 1], [2, 54, 2], [2, 162, 1], [2, 729, 2], [2, 1458, 1], [2, 2916, 1], [2, 4374, 2], [2, 6561, 1], [3, 4, 4], [3, 8, 2], [3, 16, 3], [3, 36, 1], [3, 72, 6], [3, 108, 2], [3, 144, 9], [3, 162, 1], [3, 216, 2], [3, 288, 4], [3, 324, 1], [3, 432, 6], [3, 648, 6], [3, 864, 6], [3, 1296, 6], [3, 2592, 12], [4, 78732, 2], [4, 236196, 1], [6, 108, 6], [6, 216, 6], [6, 324, 3], [6, 432, 2], [6, 648, 3], [6, 972, 8], [6, 1296, 1], [6, 1458, 6], [6, 1944, 16], [6, 2916, 9], [6, 3888, 8], [6, 5832, 25], [6, 8748, 4], [6, 11664, 10], [6, 13122, 9], [6, 17496, 2], [6, 26244, 8], [6, 52488, 2], [6, 104976, 3], [9, 108, 2], [9, 216, 4], [9, 432, 2], [9, 648, 4], [9, 972, 10], [9, 1296, 4], [9, 1944, 5], [9, 3888, 18], [9, 5832, 4], [12, 157464, 2], [12, 472392, 1], [18, 324, 2], [18, 648, 4], [18, 1296, 2], [18, 1944, 4], [18, 2916, 8], [18, 3888, 4], [18, 5832, 18], [18, 8748, 24], [18, 11664, 18], [18, 17496, 21], [18, 26244, 14], [18, 52488, 16], [36, 157464, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '5668704.km', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 16, 'conjugacy_classes_known': True, 'counter': 273, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 54, 1, 2], [2, 162, 1, 1], [2, 729, 1, 2], [2, 1458, 1, 1], [2, 2916, 1, 1], [2, 4374, 1, 2], [2, 6561, 1, 1], [3, 4, 1, 4], [3, 8, 1, 2], [3, 16, 1, 3], [3, 36, 1, 1], [3, 72, 1, 6], [3, 108, 2, 1], [3, 144, 1, 7], [3, 144, 2, 1], [3, 162, 1, 1], [3, 216, 2, 1], [3, 288, 1, 4], [3, 324, 1, 1], [3, 432, 2, 3], [3, 648, 2, 3], [3, 864, 2, 3], [3, 1296, 1, 6], [3, 2592, 1, 6], [3, 2592, 2, 3], [4, 78732, 1, 2], [4, 236196, 1, 1], [6, 108, 1, 6], [6, 216, 1, 6], [6, 324, 1, 3], [6, 432, 1, 2], [6, 648, 1, 3], [6, 972, 1, 2], [6, 972, 2, 3], [6, 1296, 1, 1], [6, 1458, 2, 3], [6, 1944, 1, 8], [6, 1944, 2, 4], [6, 2916, 1, 7], [6, 2916, 2, 1], [6, 3888, 1, 6], [6, 3888, 2, 1], [6, 5832, 1, 7], [6, 5832, 2, 9], [6, 8748, 1, 4], [6, 11664, 1, 4], [6, 11664, 2, 3], [6, 13122, 1, 3], [6, 13122, 2, 3], [6, 17496, 1, 2], [6, 26244, 1, 2], [6, 26244, 2, 3], [6, 52488, 1, 2], [6, 104976, 1, 3], [9, 108, 1, 2], [9, 216, 1, 4], [9, 432, 1, 2], [9, 648, 2, 2], [9, 972, 2, 2], [9, 972, 3, 2], [9, 1296, 2, 2], [9, 1944, 1, 5], [9, 3888, 1, 6], [9, 3888, 2, 6], [9, 5832, 1, 2], [9, 5832, 2, 1], [12, 157464, 1, 2], [12, 472392, 1, 1], [18, 324, 1, 2], [18, 648, 1, 4], [18, 1296, 1, 2], [18, 1944, 2, 2], [18, 2916, 1, 4], [18, 2916, 2, 2], [18, 3888, 2, 2], [18, 5832, 1, 12], [18, 5832, 3, 2], [18, 8748, 1, 6], [18, 8748, 2, 6], [18, 8748, 3, 2], [18, 11664, 1, 6], [18, 11664, 2, 6], [18, 17496, 1, 9], [18, 17496, 2, 6], [18, 26244, 1, 2], [18, 26244, 2, 6], [18, 52488, 1, 4], [18, 52488, 2, 3], [18, 52488, 3, 2], [36, 157464, 3, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [11, 5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 24], [24, 1, 12], [48, 0, 24], [48, 1, 12], [96, 0, 6], [96, 1, 3], [144, 0, 12], [144, 1, 12], [216, 1, 12], [288, 0, 6], [288, 1, 6], [432, 1, 12]], 'familial': False, 'frattini_label': '729.504', 'frattini_quotient': '7776.cc', 'hash': 5868977392927533895, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [36, 6, 18], 'inner_gens': [[169896969349937930797062205829531323841525, 265920363466216006568645680049807845724157, 20969948799856087611794042526813614970719], [244346113159221782194154099707146815473467, 84784991226554171514348914420873952985650, 319112745580114574583283590324581704177465], [116695113912350009884610891896795925806081, 191467976756952034845915548165589798743189, 74452114787817178376881809503970785874725]], 'inner_hash': 5868977392927533895, 'inner_nilpotent': False, 'inner_order': 5668704, 'inner_split': None, 'inner_tex': 'C_3^7.S_3^2\\wr C_2', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 22], [4, 56], [8, 34], [12, 24], [16, 14], [24, 60], [32, 1], [36, 20], [48, 42], [72, 21], [96, 9], [108, 24], [144, 28], [216, 26], [288, 12], [432, 12]], 'label': '5668704.km', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^7.S3^2wrC2', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 172, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 413, 'number_divisions': 302, 'number_normal_subgroups': 60, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 5668704, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 21411], [3, 54674], [4, 393660], [6, 1192374], [9, 122472], [12, 787320], [18, 2152008], [36, 944784]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6, 3], 'outer_gen_pows': [0, 191470132723654278316821541270060384444800], 'outer_gens': [[244050880313771703480993800928025926026400, 303652875624461801963925092714122559994, 127647213676789184065150777346692686722495], [159560307038324443133634396365666300204135, 340074529310878667792254993969540197653885, 63829429696953429413232213862075842906265]], 'outer_group': '18.3', 'outer_hash': 3, 'outer_nilpotent': False, 'outer_order': 18, 'outer_permdeg': 6, 'outer_perms': [235, 543], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times S_3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 10], [4, 30], [8, 30], [12, 8], [16, 16], [24, 28], [32, 5], [36, 20], [48, 34], [72, 19], [96, 17], [144, 17], [192, 3], [216, 20], [288, 12], [324, 8], [432, 12], [576, 3], [648, 2]], 'representations': {'PC': {'code': '348526275993519685090547546972402498932813546964456635032836532888991081827844031924224383491651042026016476983592215584655682369044586852157825830726717725150453152105010774171448195408469823249646923452031355157360874180806747969547894015303603656943035639812067854223126400064295717099496510447414995180840025862179101047252809363936458998982343510705724583761299441649926353190092208078244583942900970985518209353811769963741101527080060993363158144598984338644906907355989242511307283209390356696268398973324601971179750432338529378513694561659467536241460237853603994286420486897585703475948415', 'gens': [1, 2, 4, 6, 9, 11, 13, 14, 15, 16], 'pres': [16, 2, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 9295296, 87295425, 81, 183901058, 22674850, 33070851, 168138643, 74331875, 179, 280008964, 109176980, 98911236, 1321988, 244377221, 56294805, 48233701, 2615669, 16426725, 277, 162570246, 237823510, 16166, 19820022, 9256198, 438, 241864711, 55319, 9271, 538074152, 230262936, 137775208, 11472248, 30852648, 2159224, 351320, 424, 530173449, 304439065, 75686441, 65704377, 29724553, 8979929, 547305, 233433, 83563402, 286754714, 222051498, 80524282, 27773930, 8686746, 608362, 100458, 171754, 698, 67184651, 4479003, 7051, 630878988, 12220444, 5271612, 614092, 12535004, 303372, 18860, 684633613, 68027933, 8289853, 1967693, 11975133, 871021, 44493, 985582094, 153964830, 39191086, 63452222, 25194318, 4276894, 242062, 62798, 136254, 221199, 80621631, 13437023]}, 'Perm': {'d': 36, 'gens': [74452114787817178376881809503970785874725, 169896969349937930797062205829531323841525, 84784991226554171514348914420873952985650]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 24, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^7.S_3^2\\wr C_2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    Showing the first 100 of 413 matching records in this table.
    • id: 164385341
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 273, 'group_order': 5668704, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 164385452
      {'aut_label': '2A', 'centralizer': None, 'counter': 2, 'group_counter': 273, 'group_order': 5668704, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1629741043303725285252456672844385730, 'size': 54}
    • id: 164385563
      {'aut_label': '2A', 'centralizer': None, 'counter': 3, 'group_counter': 273, 'group_order': 5668704, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 1637963881973414448723262754016093810, 'size': 54}
    • id: 164385674
      {'aut_label': '2C', 'centralizer': None, 'counter': 4, 'group_counter': 273, 'group_order': 5668704, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 8222838669689163593585223137691331, 'size': 162}
    • id: 164385699
      {'aut_label': '2D', 'centralizer': None, 'counter': 5, 'group_counter': 273, 'group_order': 5668704, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 74452658125784662399298893914143140421163, 'size': 729}
    • id: 164385710
      {'aut_label': '2D', 'centralizer': None, 'counter': 6, 'group_counter': 273, 'group_order': 5668704, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 202100958050295697573304811581212064952389, 'size': 729}
    • id: 164385721
      {'aut_label': '2F', 'centralizer': None, 'counter': 7, 'group_counter': 273, 'group_order': 5668704, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 84494104065419258008264458663789340042826, 'size': 1458}
    • id: 164385732
      {'aut_label': '2G', 'centralizer': None, 'counter': 8, 'group_counter': 273, 'group_order': 5668704, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 351025270752337268506196281652786355844410, 'size': 2916}
    • id: 164385743
      {'aut_label': '2H', 'centralizer': None, 'counter': 9, 'group_counter': 273, 'group_order': 5668704, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 212429505388971214709829774410247340121998, 'size': 4374}
    • id: 164385342
      {'aut_label': '2H', 'centralizer': None, 'counter': 10, 'group_counter': 273, 'group_order': 5668704, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 255291982627213747737897246275077122094080, 'size': 4374}
    • id: 164385353
      {'aut_label': '2J', 'centralizer': None, 'counter': 11, 'group_counter': 273, 'group_order': 5668704, 'label': '2J', 'order': 2, 'powers': [1, 11], 'representative': 127645592296255043002419996368571952816588, 'size': 6561}
    • id: 164385364
      {'aut_label': '3A', 'centralizer': '4.J', 'counter': 12, 'group_counter': 273, 'group_order': 5668704, 'label': '3A', 'order': 3, 'powers': [12, 1], 'representative': 271353676006674126709427479550135044, 'size': 4}
    • id: 164385375
      {'aut_label': '3A', 'centralizer': '4.J', 'counter': 13, 'group_counter': 273, 'group_order': 5668704, 'label': '3B', 'order': 3, 'powers': [13, 1], 'representative': 526261674286189736370176836597907764, 'size': 4}
    • id: 164385386
      {'aut_label': '3C', 'centralizer': '4.H', 'counter': 14, 'group_counter': 273, 'group_order': 5668704, 'label': '3C', 'order': 3, 'powers': [14, 1], 'representative': 20666567304132208328166517129454676714483, 'size': 4}
    • id: 164385397
      {'aut_label': '3C', 'centralizer': '4.H', 'counter': 15, 'group_counter': 273, 'group_order': 5668704, 'label': '3D', 'order': 3, 'powers': [15, 1], 'representative': 20666567295594946898787446095608554192788, 'size': 4}
    • id: 164385408
      {'aut_label': '3E', 'centralizer': '8.J', 'counter': 16, 'group_counter': 273, 'group_order': 5668704, 'label': '3E', 'order': 3, 'powers': [16, 1], 'representative': 17683523987479404285697449984240, 'size': 8}
    • id: 164385419
      {'aut_label': '3F', 'centralizer': '8.K', 'counter': 17, 'group_counter': 273, 'group_order': 5668704, 'label': '3F', 'order': 3, 'powers': [17, 1], 'representative': 10628907036247073430557173402761975943107, 'size': 8}
    • id: 164385430
      {'aut_label': '3G', 'centralizer': '16.C', 'counter': 18, 'group_counter': 273, 'group_order': 5668704, 'label': '3G', 'order': 3, 'powers': [18, 1], 'representative': 271371359530661606113713177000119284, 'size': 16}
    • id: 164385441
      {'aut_label': '3G', 'centralizer': '16.C', 'counter': 19, 'group_counter': 273, 'group_order': 5668704, 'label': '3H', 'order': 3, 'powers': [19, 1], 'representative': 271371359918441857196987745648848883, 'size': 16}
    • id: 164385453
      {'aut_label': '3I', 'centralizer': '16.F', 'counter': 20, 'group_counter': 273, 'group_order': 5668704, 'label': '3I', 'order': 3, 'powers': [20, 1], 'representative': 20666295932772708688980490078504952448004, 'size': 16}
    • id: 164385464
      {'aut_label': '3J', 'centralizer': None, 'counter': 21, 'group_counter': 273, 'group_order': 5668704, 'label': '3J', 'order': 3, 'powers': [21, 1], 'representative': 4865804190709943043, 'size': 36}
    • id: 164385475
      {'aut_label': '3K', 'centralizer': None, 'counter': 22, 'group_counter': 273, 'group_order': 5668704, 'label': '3K', 'order': 3, 'powers': [22, 1], 'representative': 526261674673996963471294678128775107, 'size': 72}
    • id: 164385486
      {'aut_label': '3K', 'centralizer': None, 'counter': 23, 'group_counter': 273, 'group_order': 5668704, 'label': '3L', 'order': 3, 'powers': [23, 1], 'representative': 526261674286216712388020109480045508, 'size': 72}
    • id: 164385497
      {'aut_label': '3M', 'centralizer': None, 'counter': 24, 'group_counter': 273, 'group_order': 5668704, 'label': '3M', 'order': 3, 'powers': [24, 1], 'representative': 219782199337691743118678743486104, 'size': 72}
    • id: 164385508
      {'aut_label': '3M', 'centralizer': None, 'counter': 25, 'group_counter': 273, 'group_order': 5668704, 'label': '3N', 'order': 3, 'powers': [25, 1], 'representative': 228928849703019176400386411518200, 'size': 72}
    • id: 164385519
      {'aut_label': '3M', 'centralizer': None, 'counter': 26, 'group_counter': 273, 'group_order': 5668704, 'label': '3O', 'order': 3, 'powers': [26, 1], 'representative': 20666296161701139587080495086540216766200, 'size': 72}
    • id: 164385530
      {'aut_label': '3P', 'centralizer': None, 'counter': 27, 'group_counter': 273, 'group_order': 5668704, 'label': '3P', 'order': 3, 'powers': [27, 1], 'representative': 711468261504244, 'size': 72}
    • id: 164385541
      {'aut_label': '3Q1', 'centralizer': None, 'counter': 28, 'group_counter': 273, 'group_order': 5668704, 'label': '3Q1', 'order': 3, 'powers': [29, 1], 'representative': 4866180719976656788, 'size': 108}
    • id: 164385552
      {'aut_label': '3Q1', 'centralizer': None, 'counter': 29, 'group_counter': 273, 'group_order': 5668704, 'label': '3Q-1', 'order': 3, 'powers': [28, 1], 'representative': 2555258657798292003, 'size': 108}
    • id: 164385564
      {'aut_label': '3R', 'centralizer': None, 'counter': 30, 'group_counter': 273, 'group_order': 5668704, 'label': '3R', 'order': 3, 'powers': [30, 1], 'representative': 17683523987484270089888159927283, 'size': 144}
    • id: 164385575
      {'aut_label': '3S', 'centralizer': None, 'counter': 31, 'group_counter': 273, 'group_order': 5668704, 'label': '3S', 'order': 3, 'powers': [31, 1], 'representative': 148607638891963654929543486585385026150964, 'size': 144}
    • id: 164385586
      {'aut_label': '3S', 'centralizer': None, 'counter': 32, 'group_counter': 273, 'group_order': 5668704, 'label': '3T', 'order': 3, 'powers': [32, 1], 'representative': 127941088051193473386555640248084818595987, 'size': 144}
    • id: 164385597
      {'aut_label': '3S', 'centralizer': None, 'counter': 33, 'group_counter': 273, 'group_order': 5668704, 'label': '3U', 'order': 3, 'powers': [33, 1], 'representative': 10635434149378833858657174144988471004403, 'size': 144}
    • id: 164385608
      {'aut_label': '3S', 'centralizer': None, 'counter': 34, 'group_counter': 273, 'group_order': 5668704, 'label': '3V', 'order': 3, 'powers': [34, 1], 'representative': 10628380783120161439791288085454859381814, 'size': 144}
    • id: 164385619
      {'aut_label': '3S', 'centralizer': None, 'counter': 35, 'group_counter': 273, 'group_order': 5668704, 'label': '3W', 'order': 3, 'powers': [35, 1], 'representative': 10628380774583287790660745779162205394434, 'size': 144}
    • id: 164385630
      {'aut_label': '3S', 'centralizer': None, 'counter': 36, 'group_counter': 273, 'group_order': 5668704, 'label': '3X', 'order': 3, 'powers': [36, 1], 'representative': 148607383975428501791781854832038152880644, 'size': 144}
    • id: 164385641
      {'aut_label': '3Y1', 'centralizer': None, 'counter': 37, 'group_counter': 273, 'group_order': 5668704, 'label': '3Y1', 'order': 3, 'powers': [38, 1], 'representative': 271353676006674129021060997535846548, 'size': 144}
    • id: 164385652
      {'aut_label': '3Y1', 'centralizer': None, 'counter': 38, 'group_counter': 273, 'group_order': 5668704, 'label': '3Y-1', 'order': 3, 'powers': [37, 1], 'representative': 526261674673969985142905872334976243, 'size': 144}
    • id: 164385663
      {'aut_label': '3Z', 'centralizer': None, 'counter': 39, 'group_counter': 273, 'group_order': 5668704, 'label': '3Z', 'order': 3, 'powers': [39, 1], 'representative': 51706588401663156909507, 'size': 162}
    • id: 164385675
      {'aut_label': '3AA1', 'centralizer': None, 'counter': 40, 'group_counter': 273, 'group_order': 5668704, 'label': '3AA1', 'order': 3, 'powers': [41, 1], 'representative': 17683524039188303567577205482484, 'size': 216}
    • id: 164385686
      {'aut_label': '3AA1', 'centralizer': None, 'counter': 41, 'group_counter': 273, 'group_order': 5668704, 'label': '3AA-1', 'order': 3, 'powers': [40, 1], 'representative': 9146650365329988540365582445507, 'size': 216}
    • id: 164385691
      {'aut_label': '3AB', 'centralizer': None, 'counter': 42, 'group_counter': 273, 'group_order': 5668704, 'label': '3AB', 'order': 3, 'powers': [42, 1], 'representative': 9147069168003469733894918288788, 'size': 288}
    • id: 164385692
      {'aut_label': '3AC', 'centralizer': None, 'counter': 43, 'group_counter': 273, 'group_order': 5668704, 'label': '3AC', 'order': 3, 'powers': [43, 1], 'representative': 9151699008085329105661629468116, 'size': 288}
    • id: 164385693
      {'aut_label': '3AC', 'centralizer': None, 'counter': 44, 'group_counter': 273, 'group_order': 5668704, 'label': '3AD', 'order': 3, 'powers': [44, 1], 'representative': 9151699008090194909584577400835, 'size': 288}
    • id: 164385694
      {'aut_label': '3AC', 'centralizer': None, 'counter': 45, 'group_counter': 273, 'group_order': 5668704, 'label': '3AE', 'order': 3, 'powers': [45, 1], 'representative': 271362827286879540868596345254904836, 'size': 288}
    • id: 164385695
      {'aut_label': '3AF', 'centralizer': None, 'counter': 46, 'group_counter': 273, 'group_order': 5668704, 'label': '3AF', 'order': 3, 'powers': [46, 1], 'representative': 10628380783110079667896810338204057680788, 'size': 324}
    • id: 164385696
      {'aut_label': '3AG1', 'centralizer': None, 'counter': 47, 'group_counter': 273, 'group_order': 5668704, 'label': '3AG1', 'order': 3, 'powers': [48, 1], 'representative': 237466529908093400239211500068744, 'size': 432}
    • id: 164385697
      {'aut_label': '3AG1', 'centralizer': None, 'counter': 48, 'group_counter': 273, 'group_order': 5668704, 'label': '3AG-1', 'order': 3, 'powers': [47, 1], 'representative': 110197035991352622155814092926224, 'size': 432}
    • id: 164385698
      {'aut_label': '3AG1', 'centralizer': None, 'counter': 49, 'group_counter': 273, 'group_order': 5668704, 'label': '3AH1', 'order': 3, 'powers': [50, 1], 'representative': 20669826741063932491318326503231618780160, 'size': 432}
    • id: 164385700
      {'aut_label': '3AG1', 'centralizer': None, 'counter': 50, 'group_counter': 273, 'group_order': 5668704, 'label': '3AH-1', 'order': 3, 'powers': [49, 1], 'representative': 10635162778019721948023062694934710575920, 'size': 432}
    • id: 164385701
      {'aut_label': '3AG1', 'centralizer': None, 'counter': 51, 'group_counter': 273, 'group_order': 5668704, 'label': '3AI1', 'order': 3, 'powers': [52, 1], 'representative': 271353681024348416552811144137554292, 'size': 432}
    • id: 164385702
      {'aut_label': '3AG1', 'centralizer': None, 'counter': 52, 'group_counter': 273, 'group_order': 5668704, 'label': '3AI-1', 'order': 3, 'powers': [51, 1], 'representative': 526261684336966189089608901172917570, 'size': 432}
    • id: 164385703
      {'aut_label': '3AJ1', 'centralizer': None, 'counter': 53, 'group_counter': 273, 'group_order': 5668704, 'label': '3AJ1', 'order': 3, 'powers': [54, 1], 'representative': 148607638891963654956514638247950226122240, 'size': 648}
    • id: 164385704
      {'aut_label': '3AJ1', 'centralizer': None, 'counter': 54, 'group_counter': 273, 'group_order': 5668704, 'label': '3AJ-1', 'order': 3, 'powers': [53, 1], 'representative': 255585857039191330898341255127597151290160, 'size': 648}
    • id: 164385705
      {'aut_label': '3AJ1', 'centralizer': None, 'counter': 55, 'group_counter': 273, 'group_order': 5668704, 'label': '3AK1', 'order': 3, 'powers': [56, 1], 'representative': 20672823046514214756912680551799979785760, 'size': 648}
    • id: 164385706
      {'aut_label': '3AJ1', 'centralizer': None, 'counter': 56, 'group_counter': 273, 'group_order': 5668704, 'label': '3AK-1', 'order': 3, 'powers': [55, 1], 'representative': 10632166499398388622663793965698197727424, 'size': 648}
    • id: 164385707
      {'aut_label': '3AJ1', 'centralizer': None, 'counter': 57, 'group_counter': 273, 'group_order': 5668704, 'label': '3AL1', 'order': 3, 'powers': [58, 1], 'representative': 6527104595693388875150176367468297763, 'size': 648}
    • id: 164385708
      {'aut_label': '3AJ1', 'centralizer': None, 'counter': 58, 'group_counter': 273, 'group_order': 5668704, 'label': '3AL-1', 'order': 3, 'powers': [57, 1], 'representative': 3785716289922199296407175095584991428, 'size': 648}
    • id: 164385709
      {'aut_label': '3AM1', 'centralizer': None, 'counter': 59, 'group_counter': 273, 'group_order': 5668704, 'label': '3AM1', 'order': 3, 'powers': [60, 1], 'representative': 9151699035061346572405244892119, 'size': 864}
    • id: 164385711
      {'aut_label': '3AM1', 'centralizer': None, 'counter': 60, 'group_counter': 273, 'group_order': 5668704, 'label': '3AM-1', 'order': 3, 'powers': [59, 1], 'representative': 9151699059789362583338220981715, 'size': 864}
    • id: 164385712
      {'aut_label': '3AM1', 'centralizer': None, 'counter': 61, 'group_counter': 273, 'group_order': 5668704, 'label': '3AN1', 'order': 3, 'powers': [62, 1], 'representative': 9151699035066212376340646866436, 'size': 864}
    • id: 164385713
      {'aut_label': '3AM1', 'centralizer': None, 'counter': 62, 'group_counter': 273, 'group_order': 5668704, 'label': '3AN-1', 'order': 3, 'powers': [61, 1], 'representative': 9151699059794228387528930808839, 'size': 864}
    • id: 164385714
      {'aut_label': '3AM1', 'centralizer': None, 'counter': 63, 'group_counter': 273, 'group_order': 5668704, 'label': '3AO1', 'order': 3, 'powers': [64, 1], 'representative': 271362827286906516886063088870328839, 'size': 864}
    • id: 164385715
      {'aut_label': '3AM1', 'centralizer': None, 'counter': 64, 'group_counter': 273, 'group_order': 5668704, 'label': '3AO-1', 'order': 3, 'powers': [63, 1], 'representative': 271362827286931244902074021846418435, 'size': 864}
    • id: 164385716
      {'aut_label': '3AP', 'centralizer': None, 'counter': 65, 'group_counter': 273, 'group_order': 5668704, 'label': '3AP', 'order': 3, 'powers': [65, 1], 'representative': 127941088033513739693639537412268243473236, 'size': 1296}
    • id: 164385717
      {'aut_label': '3AP', 'centralizer': None, 'counter': 66, 'group_counter': 273, 'group_order': 5668704, 'label': '3AQ', 'order': 3, 'powers': [66, 1], 'representative': 137978731847183886001112180699091345880291, 'size': 1296}
    • id: 164385718
      {'aut_label': '3AP', 'centralizer': None, 'counter': 67, 'group_counter': 273, 'group_order': 5668704, 'label': '3AR', 'order': 3, 'powers': [67, 1], 'representative': 137979003210006512018143682199023733781076, 'size': 1296}
    • id: 164385719
      {'aut_label': '3AS', 'centralizer': None, 'counter': 68, 'group_counter': 273, 'group_order': 5668704, 'label': '3AS', 'order': 3, 'powers': [68, 1], 'representative': 20666296152554908026677099001118974645144, 'size': 1296}
    • id: 164385720
      {'aut_label': '3AS', 'centralizer': None, 'counter': 69, 'group_counter': 273, 'group_order': 5668704, 'label': '3AT', 'order': 3, 'powers': [69, 1], 'representative': 20666296051505780748849330636549357739444, 'size': 1296}
    • id: 164385722
      {'aut_label': '3AS', 'centralizer': None, 'counter': 70, 'group_counter': 273, 'group_order': 5668704, 'label': '3AU', 'order': 3, 'powers': [70, 1], 'representative': 10628380783114321754706158449347726257879, 'size': 1296}
    • id: 164385723
      {'aut_label': '3AV', 'centralizer': None, 'counter': 71, 'group_counter': 273, 'group_order': 5668704, 'label': '3AV', 'order': 3, 'powers': [71, 1], 'representative': 110200407589056648278193154099445, 'size': 2592}
    • id: 164385724
      {'aut_label': '3AW', 'centralizer': None, 'counter': 72, 'group_counter': 273, 'group_order': 5668704, 'label': '3AW', 'order': 3, 'powers': [72, 1], 'representative': 110200407589061513747270512553521, 'size': 2592}
    • id: 164385725
      {'aut_label': '3AV', 'centralizer': None, 'counter': 73, 'group_counter': 273, 'group_order': 5668704, 'label': '3AX', 'order': 3, 'powers': [73, 1], 'representative': 110200407640765547225214858703925, 'size': 2592}
    • id: 164385726
      {'aut_label': '3AW', 'centralizer': None, 'counter': 74, 'group_counter': 273, 'group_order': 5668704, 'label': '3AY', 'order': 3, 'powers': [74, 1], 'representative': 271463875995460512187434031190057522, 'size': 2592}
    • id: 164385727
      {'aut_label': '3AW', 'centralizer': None, 'counter': 75, 'group_counter': 273, 'group_order': 5668704, 'label': '3AZ', 'order': 3, 'powers': [75, 1], 'representative': 271463875995512216221246565817833762, 'size': 2592}
    • id: 164385728
      {'aut_label': '3AV', 'centralizer': None, 'counter': 76, 'group_counter': 273, 'group_order': 5668704, 'label': '3BA', 'order': 3, 'powers': [76, 1], 'representative': 10628652229301744558002474847767089065521, 'size': 2592}
    • id: 164385729
      {'aut_label': '3BB1', 'centralizer': None, 'counter': 77, 'group_counter': 273, 'group_order': 5668704, 'label': '3BB1', 'order': 3, 'powers': [78, 1], 'representative': 110200407589061514082128556073762, 'size': 2592}
    • id: 164385730
      {'aut_label': '3BB1', 'centralizer': None, 'counter': 78, 'group_counter': 273, 'group_order': 5668704, 'label': '3BB-1', 'order': 3, 'powers': [77, 1], 'representative': 110200407589061514458819725328069, 'size': 2592}
    • id: 164385731
      {'aut_label': '3BB1', 'centralizer': None, 'counter': 79, 'group_counter': 273, 'group_order': 5668704, 'label': '3BC1', 'order': 3, 'powers': [80, 1], 'representative': 271463875995460512187768876779536165, 'size': 2592}
    • id: 164385733
      {'aut_label': '3BB1', 'centralizer': None, 'counter': 80, 'group_counter': 273, 'group_order': 5668704, 'label': '3BC-1', 'order': 3, 'powers': [79, 1], 'representative': 271463875995460512188145312640937665, 'size': 2592}
    • id: 164385734
      {'aut_label': '3BB1', 'centralizer': None, 'counter': 81, 'group_counter': 273, 'group_order': 5668704, 'label': '3BD1', 'order': 3, 'powers': [82, 1], 'representative': 271463875995512216220911707774313521, 'size': 2592}
    • id: 164385735
      {'aut_label': '3BB1', 'centralizer': None, 'counter': 82, 'group_counter': 273, 'group_order': 5668704, 'label': '3BD-1', 'order': 3, 'powers': [81, 1], 'representative': 271463875995512216221623256987088069, 'size': 2592}
    • id: 164385736
      {'aut_label': '4A', 'centralizer': None, 'counter': 83, 'group_counter': 273, 'group_order': 5668704, 'label': '4A', 'order': 4, 'powers': [5, 83], 'representative': 287208327276726815149641904713610568405044, 'size': 78732}
    • id: 164385737
      {'aut_label': '4A', 'centralizer': None, 'counter': 84, 'group_counter': 273, 'group_order': 5668704, 'label': '4B', 'order': 4, 'powers': [6, 84], 'representative': 244044904816700462494346675783168560959837, 'size': 78732}
    • id: 164385738
      {'aut_label': '4C', 'centralizer': None, 'counter': 85, 'group_counter': 273, 'group_order': 5668704, 'label': '4C', 'order': 4, 'powers': [11, 85], 'representative': 308168778084700510060070043920140804083146, 'size': 236196}
    • id: 164385739
      {'aut_label': '6A', 'centralizer': None, 'counter': 86, 'group_counter': 273, 'group_order': 5668704, 'label': '6A', 'order': 6, 'powers': [12, 2], 'representative': 4897391031283176743393918353506468212, 'size': 108}
    • id: 164385740
      {'aut_label': '6A', 'centralizer': None, 'counter': 87, 'group_counter': 273, 'group_order': 5668704, 'label': '6B', 'order': 6, 'powers': [13, 3], 'representative': 8148595335662763353453425267800822214, 'size': 108}
    • id: 164385741
      {'aut_label': '6C', 'centralizer': None, 'counter': 88, 'group_counter': 273, 'group_order': 5668704, 'label': '6C', 'order': 6, 'powers': [12, 2], 'representative': 319408496508940343376539217779969870923467, 'size': 108}
    • id: 164385742
      {'aut_label': '6C', 'centralizer': None, 'counter': 89, 'group_counter': 273, 'group_order': 5668704, 'label': '6D', 'order': 6, 'powers': [13, 3], 'representative': 20671456472320674738623759766006192282211, 'size': 108}
    • id: 164385744
      {'aut_label': '6E', 'centralizer': None, 'counter': 90, 'group_counter': 273, 'group_order': 5668704, 'label': '6E', 'order': 6, 'powers': [12, 3], 'representative': 63823725616727383250597951377530044510667, 'size': 108}
    • id: 164385745
      {'aut_label': '6E', 'centralizer': None, 'counter': 91, 'group_counter': 273, 'group_order': 5668704, 'label': '6F', 'order': 6, 'powers': [13, 2], 'representative': 20667925691499117599073976884079322235570, 'size': 108}
    • id: 164385746
      {'aut_label': '6G', 'centralizer': None, 'counter': 92, 'group_counter': 273, 'group_order': 5668704, 'label': '6G', 'order': 6, 'powers': [16, 2], 'representative': 1629750189954063636668983092820577874, 'size': 216}
    • id: 164385747
      {'aut_label': '6G', 'centralizer': None, 'counter': 93, 'group_counter': 273, 'group_order': 5668704, 'label': '6H', 'order': 6, 'powers': [16, 3], 'representative': 1637973028623752800139789173992285954, 'size': 216}
    • id: 164385748
      {'aut_label': '6I', 'centralizer': None, 'counter': 94, 'group_counter': 273, 'group_order': 5668704, 'label': '6I', 'order': 6, 'powers': [17, 2], 'representative': 212134790728555763106294856449300696721204, 'size': 216}
    • id: 164385749
      {'aut_label': '6J', 'centralizer': None, 'counter': 95, 'group_counter': 273, 'group_order': 5668704, 'label': '6J', 'order': 6, 'powers': [14, 3], 'representative': 63823725634410519457826272388658845765164, 'size': 216}
    • id: 164385750
      {'aut_label': '6I', 'centralizer': None, 'counter': 96, 'group_counter': 273, 'group_order': 5668704, 'label': '6K', 'order': 6, 'powers': [17, 3], 'representative': 329741389677523180116566204858608152981124, 'size': 216}
    • id: 164385751
      {'aut_label': '6J', 'centralizer': None, 'counter': 97, 'group_counter': 273, 'group_order': 5668704, 'label': '6L', 'order': 6, 'powers': [15, 2], 'representative': 329446156759751343220369518389881785966988, 'size': 216}
    • id: 164385752
      {'aut_label': '6M', 'centralizer': None, 'counter': 98, 'group_counter': 273, 'group_order': 5668704, 'label': '6M', 'order': 6, 'powers': [21, 4], 'representative': 8222838669689166148132506079791092, 'size': 324}
    • id: 164385753
      {'aut_label': '6N', 'centralizer': None, 'counter': 99, 'group_counter': 273, 'group_order': 5668704, 'label': '6N', 'order': 6, 'powers': [12, 4], 'representative': 10631903368562277074936670070524826414055, 'size': 324}
    • id: 164385343
      {'aut_label': '6N', 'centralizer': None, 'counter': 100, 'group_counter': 273, 'group_order': 5668704, 'label': '6O', 'order': 6, 'powers': [13, 4], 'representative': 275956920164082254652467086935759625486227, 'size': 324}
  • group 5668704.km does not appear in gps_qchar
  • group 5668704.km does not appear in gps_char
  • gps_subgroup_search • Show schema
    Showing the first 100 of 209 matching records in this table.
    • id: 227357450
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 5668704, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '5668704.km.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5668704.km', 'subgroup_hash': 5868977392927533895, 'subgroup_order': 5668704, 'subgroup_tex': 'C_3^7.S_3^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 227357561
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2834352, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.2.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2834352.qf', 'subgroup_hash': 6223660714353478061, 'subgroup_order': 2834352, 'subgroup_tex': 'C_3^7.S_3^2:S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 227357582
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2834352, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2834352.nt', 'subgroup_hash': 5622436048754501560, 'subgroup_order': 2834352, 'subgroup_tex': 'C_3^6.(C_3^3\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357593
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 2834352, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.2.C', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8651497143556447312, 'subgroup_order': 2834352, 'subgroup_tex': 'C_3^6.C_3^5.C_2^4', 'supersolvable': True, 'sylow': 0}
    • id: 227357604
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 2834352, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.2.D', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2834352.ol', 'subgroup_hash': 2860796933579623202, 'subgroup_order': 2834352, 'subgroup_tex': 'C_3^6.C_3^5:(C_2\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 227357615
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 2834352, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.2.E', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2834352.ot', 'subgroup_hash': 6268035797580749796, 'subgroup_order': 2834352, 'subgroup_tex': 'C_3^7.(C_3^2\\wr C_2.D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 227357626
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 944784, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1889568.ou', 'subgroup_hash': 4392743754135259478, 'subgroup_order': 1889568, 'subgroup_tex': 'C_3^4.C_3^4:D_6\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 227357637
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1417176, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5321029721227134822, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^6.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357648
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 1417176, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9056352482245890747, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^6.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357451
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 1417176, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1417176.ra', 'subgroup_hash': 4062724127760401953, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^7.C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357462
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1417176, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1417176.sa', 'subgroup_hash': 122078750681534586, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^6.C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 227357473
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 1417176, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1417176.ss', 'subgroup_hash': 8206572979179734459, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^5.\\He_3^2:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
    • id: 227357484
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 8023927646514906754, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^6.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357495
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 8641243744075444467, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^6.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357506
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1417176.qk', 'subgroup_hash': 50716598982314678, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^7.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357517
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 5321029721227134822, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^6.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357528
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 2441864863117863475, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^5.C_3^4.C_6^2.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 227357539
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 6072496213113375122, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^6.C_3^5.D_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357550
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1417176.rl', 'subgroup_hash': 3638894387430491237, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^6.C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 227357562
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.4.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '1417176.tt', 'subgroup_hash': 7685357989358497988, 'subgroup_order': 1417176, 'subgroup_tex': 'C_3^5.\\He_3^2:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357573
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 944784, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5240688454913756406, 'subgroup_order': 944784, 'subgroup_tex': 'C_3^6.C_3^4.C_2^4', 'supersolvable': True, 'sylow': 0}
    • id: 227357574
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '944784.pu', 'subgroup_hash': 3898588006810224927, 'subgroup_order': 944784, 'subgroup_tex': 'C_3^6.S_3^3:S_3', 'supersolvable': False, 'sylow': 0}
    • id: 227357575
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 472392, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '944784.rx', 'subgroup_hash': 4214627173336113295, 'subgroup_order': 944784, 'subgroup_tex': 'C_3^6.S_3^2:S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 227357576
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 472392, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.6.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '944784.qn', 'subgroup_hash': 6944014194163553630, 'subgroup_order': 944784, 'subgroup_tex': 'C_3^6.(C_3^2\\times S_3^2):C_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357577
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.6.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8123512313797299975, 'subgroup_order': 944784, 'subgroup_tex': 'C_3^5.C_3^5.C_2^4', 'supersolvable': True, 'sylow': 0}
    • id: 227357578
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 472392, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.6.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '944784.qs', 'subgroup_hash': 5280256047558596431, 'subgroup_order': 944784, 'subgroup_tex': 'C_3^6.C_3^4:(C_2\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 227357579
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 472392, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.6.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '944784.ra', 'subgroup_hash': 2258758172757652764, 'subgroup_order': 944784, 'subgroup_tex': 'C_3^6.(C_3^2\\wr C_2.D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 227357580
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9169348750833008289, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^6.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357581
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 708588, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4782082968074014173, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^6.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357583
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 708588, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7750764134478793408, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^6.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357584
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 708588, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1334165307839367202, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^6.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357585
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 708588, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1334165307839367202, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^6.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357586
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 636498046246424311, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^5.C_3^4.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357587
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 354294, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 3598869452480758056, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^5.C_3^4.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357588
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 3598869452480758056, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^5.C_3^4.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357589
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 354294, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 4573177861107268705, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^6.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357590
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 1646825583857518866, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^5.C_3^4.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357591
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 9169348750833008289, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^5.C_3^4.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357592
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 354294, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 2842237393265463321, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^5.C_3^4.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357594
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 9156835026200020781, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^6.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357595
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 354294, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '708588.je', 'subgroup_hash': 6488202608253385818, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^7.C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357596
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 354294, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '708588.jn', 'subgroup_hash': 8626870096490432248, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^7.C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357597
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 7750764134478793408, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^6.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357598
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 354294, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 5900733780333578990, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^6.C_3^4.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 227357599
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 354294, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.8.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': None, 'subgroup_hash': 939647961878922444, 'subgroup_order': 708588, 'subgroup_tex': 'C_3^7.C_3^4.C_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357600
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.9.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '629856.ir', 'subgroup_hash': 6201463762306670485, 'subgroup_order': 629856, 'subgroup_tex': 'C_3^5.S_3^2\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 227357601
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 472392, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6905203737013556544, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357602
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 472392, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5131880999885285874, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357603
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1264860683393913080, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357605
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9014474091950446512, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357606
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9014474091950446512, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357607
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1648037460977361909, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357608
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8863972233645955177, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357609
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1936029128012013436, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357610
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9161907214244657750, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357611
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9161907214244657750, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357612
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5601228943079960688, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^4.C_3^4.C_6^2.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 227357613
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7229658667299740020, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^3.C_3^5.C_6^2.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 227357614
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1287306702764311279, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357616
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '472392.rw', 'subgroup_hash': 4458908981959553522, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357617
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '472392.rj', 'subgroup_hash': 2127448416139554951, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357618
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '472392.sd', 'subgroup_hash': 8081878740982559892, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357619
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '472392.oz', 'subgroup_hash': 6525094421611175051, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^7.S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
    • id: 227357620
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3908815333068829280, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357621
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6625195188716183739, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357622
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3908815333068829280, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357623
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6625195188716183739, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357624
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6905203737013556544, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357625
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2839060943748059249, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357627
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2839060943748059249, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^4.C_3^4.C_6^2.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 227357628
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 458229089664279412, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357629
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5851015536169841837, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357630
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9031992988704511565, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^4.C_6.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 227357631
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3569802622480348031, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357632
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7438132729563082098, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^5.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357633
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1051888667455251132, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.D_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357634
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '472392.rf', 'subgroup_hash': 4710146064020134651, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^7.S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
    • id: 227357635
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '472392.sn', 'subgroup_hash': 1440794149021317160, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 227357636
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '472392.qa', 'subgroup_hash': 7363779358303002187, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^4.C_3^5:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 227357638
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '472392.po', 'subgroup_hash': 8533908772078418872, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^7.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357639
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '472392.qi', 'subgroup_hash': 5250080096108689013, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^4.C_3^5:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 227357640
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '472392.sf', 'subgroup_hash': 5139320985986329917, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 227357641
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '472392.sq', 'subgroup_hash': 3652164612811462139, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 227357642
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '472392.sw', 'subgroup_hash': 1705182358895373303, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4:(C_2\\times C_4)', 'supersolvable': False, 'sylow': 0}
    • id: 227357643
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.12.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '472392.tf', 'subgroup_hash': 744418981690215363, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357644
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 354294, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.16.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8850084279543578570, 'subgroup_order': 354294, 'subgroup_tex': 'C_3^6.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 227357645
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 354294, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.16.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2032264371956513491, 'subgroup_order': 354294, 'subgroup_tex': 'C_3^6.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 227357646
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.16.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4166349827646400354, 'subgroup_order': 354294, 'subgroup_tex': 'C_3^4.C_3^5.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 227357647
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.16.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5662261935909873363, 'subgroup_order': 354294, 'subgroup_tex': 'C_3^6.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 227357649
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.16.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8850084279543578570, 'subgroup_order': 354294, 'subgroup_tex': 'C_3^5.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 227357650
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.16.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7170140485408563300, 'subgroup_order': 354294, 'subgroup_tex': 'C_3^7.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 227357651
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 177147, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.16.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6770419095752497969, 'subgroup_order': 354294, 'subgroup_tex': 'C_3^6.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 227357652
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '314928.nj', 'subgroup_hash': 8520627775546397226, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^4.C_{18}^2:D_6', 'supersolvable': False, 'sylow': 0}
    • id: 227357653
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '314928.oh', 'subgroup_hash': 4484621401393863328, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^7.C_6^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357654
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.18.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '314928.lj', 'subgroup_hash': 284177892432782144, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^4.D_9^2:D_6', 'supersolvable': False, 'sylow': 0}
    • id: 227357655
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.18.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '314928.mv', 'subgroup_hash': 8227127147000061400, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^7.S_3^2:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 227357656
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.18.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '314928.pl', 'subgroup_hash': 2343006311215618144, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^4:D_9^2.D_6', 'supersolvable': False, 'sylow': 0}
    • id: 227357657
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 243, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.18.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3334623475260905592, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^4.C_3^5.C_2^4', 'supersolvable': True, 'sylow': 0}
    • id: 227357658
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.18.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7005187708939152454, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^5.C_3^4.C_2^4', 'supersolvable': True, 'sylow': 0}
    • id: 227357452
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5668704.km', 'ambient_counter': 273, 'ambient_order': 5668704, 'ambient_tex': 'C_3^7.S_3^2\\wr C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '5668704.km.18.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7005187708939152454, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^4.C_3^5.C_2^4', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 209 matching records in this table.
    • id: 227357450
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [65, 1875, 28, 144], 'generators': [10635162896757390993414566838516740831429, 169896969349937930797062205829531323841525, 376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 74452114787817178376881809503970785874725, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 534484512537076226482945047212498519, 2554547201990829364, 339786638473518681688268813323916449252414, 5048696709930422514535413716, 295767283857029887135120785100220451842, 127889352434221996633002663056068], 'label': '5668704.km.1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '5668704.km'}
    • id: 227357451
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '4.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.C', 'coset_action_label': None, 'count': 1, 'diagramx': [402, 3422, 595, 2179], 'generators': [9146650338351416526419976192144, 10635162896757390993414566838516740831429, 376784574566547, 10628380774572399460569719951356729305744, 806582922253211364573312003, 271353676394454377792702048198864643, 244347471345430201299556277355199039648078, 148607112713014174806923992600527462032787, 26976017843272882137744, 2554547201990829364, 339786638473518681688268813323916449252414, 5048696709930422514535413716, 295767283857029887135120785100220451842, 127889352434221996633002663056068], 'label': '5668704.km.4.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.C', 'subgroup_fusion': None, 'weyl_group': '5668704.km'}
    • id: 227357452
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '18.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1149, -1, 5355, -1], 'generators': [271353676006674126709427479550135044, 26976017843272882137744, 17683523987479404285697449984240, 2554547201990829364, 212431135120216601427188089883713359636958, 319113272042934768006328024585537002226085, 295767283857029887135120785100220451842, 534484512537076226482945047212498519, 148607112713014174806923992600527462032787, 20666295941918940224660736668129004057744, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.18.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.h1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.H', 'subgroup_fusion': None, 'weyl_group': '629856.ir'}
    • id: 227357453
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '18.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 18, 'diagramx': [174, -1, 4917, -1], 'generators': [376784574566547, 319113272033792747508060516188947809893281, 20666295941918940224660736668129004057744, 271353676006674126709427479550135044, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 339781197680129416530175953025654463396404, 5048696709930422514535413716, 17683523987479404285697449984240, 295767411136605575774997618656765935294], 'label': '5668704.km.18.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.I', 'old_label': '18.i1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.I', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357454
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '18.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 12, 'diagramx': [649, -1, 5130, -1], 'generators': [271353676006674126709427479550135044, 26976017843272882137744, 534484512537076226482568356043243971, 319116005199262768863415525693748376007107, 17683523987479404285697449984240, 2554547201990829364, 295767283857029887135120073551007677585, 148607112713014174806923992600527462032787, 5048696709930422514535413716, 201805462074313976155119614352623181022109, 20666295941918940224660736668129004057744, 418802671169936795924582404, 20669826758750828128195554838476720758855], 'label': '5668704.km.18.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '18.j1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.J', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357455
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '18.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 18, 'diagramx': [529, -1, 5077, -1], 'generators': [271353676006674126709427479550135044, 26976017843272882137744, 17683523987479404285697449984240, 20669826758755473373682980260703572554754, 2554547201990829364, 212431135120216601427188089883713359636958, 295767512176102873954850487175411835786, 534484512537076226482945047212498519, 127946784009629170692381711490250973056396, 244345289905911105840262258515967624599117, 20666295941918940224660736668129004057744, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.18.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.k1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.K', 'subgroup_fusion': None, 'weyl_group': '629856.ir'}
    • id: 227357456
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '18.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 18, 'diagramx': [299, -1, 4973, -1], 'generators': [271353676006674126709427479550135044, 26976017843272882137744, 17683523987479404285697449984240, 169893446764487007195349730575692342226085, 20669826758755473373682980260703572554754, 2554547201990829364, 212431135120216601427188089883713359636958, 295767512176102873954850487175411835786, 534484512537076226482945047212498519, 127946784009629170692381711490250973056396, 20666295941918940224660736668129004057744, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.18.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.l1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.L', 'subgroup_fusion': None, 'weyl_group': '629856.ir'}
    • id: 227357457
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 2, 'diagramx': [7734, 3185, 8982, 6136], 'generators': [10635162896757390993414566838516740831429, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 74451580303304641327646449112776515611524, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 339786638473518681688268813323916449252414, 5048696709930422514535413716, 127889352434221996633002663056068], 'label': '5668704.km.24.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.A', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357458
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.B', 'coset_action_label': None, 'count': 1, 'diagramx': [45, 1592, 5527, 5880], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 534484512537076226482568356043243971, 2554547201990829364, 295767283857029887135120073551007677585, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.B', 'subgroup_fusion': None, 'weyl_group': '5668704.km'}
    • id: 227357459
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.C', 'coset_action_label': None, 'count': 2, 'diagramx': [9851, 7780, 9933, 6872], 'generators': [10635162896757390993414566838516740831429, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 84785262644007545316582570272139665657546, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 339786638473518681688268813323916449252414, 5048696709930422514535413716, 127889352434221996633002663056068], 'label': '5668704.km.24.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.C', 'subgroup_fusion': None, 'weyl_group': '5668704.km'}
    • id: 227357460
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.D', 'coset_action_label': None, 'count': 1, 'diagramx': [8753, 4777, 9440, 6391], 'generators': [339786638473518681688268813323916449252414, 17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120073551007677585, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.d1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.D', 'subgroup_fusion': None, 'weyl_group': '5668704.km'}
    • id: 227357461
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.E', 'coset_action_label': None, 'count': 1, 'diagramx': [8856, 6279, 9486, 6631], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120073551007677585, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 329748986437009090077196053098679447923788, 418802671169936795924582404], 'label': '5668704.km.24.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.e1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.E', 'subgroup_fusion': None, 'weyl_group': '5668704.km'}
    • id: 227357462
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '4.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '4.D', 'coset_action_label': None, 'count': 2, 'diagramx': [751, 6833, 752, 2726], 'generators': [9146650338351416526419976192144, 10635162896757390993414566838516740831429, 169896706219100981592342488567959891660804, 376784574566547, 10628380774572399460569719951356729305744, 806582922253211364573312003, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 26976017843272882137744, 2554547201990829364, 339786638473518681688268813323916449252414, 5048696709930422514535413716, 295767283857029887135120785100220451842, 127889352434221996633002663056068], 'label': '5668704.km.4.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.D', 'subgroup_fusion': None, 'weyl_group': '5668704.km'}
    • id: 227357463
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [9742, -1, 9884, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 74452114787817178376881809503970785874725, 534484512537076226482945047212498519, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.f1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.F', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357464
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3706, -1, 7172, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 74452114787817178376881809503970785874725, 271353676394454377792702048198864643, 319114375367255915111659889580924124767838, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 10635162896760747023547559786028911671843], 'label': '5668704.km.24.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.g1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.G', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357465
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3821, -1, 7224, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 127880141203136872883474036196720, 74452114787817178376881809503970785874725, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 319114638498092864316372307090056106632507, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.h1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.H', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357466
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1757, -1, 6296, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 20964796619571340395355542052596559051560, 2554547201990829364, 74451580303304641300670431646207293057923, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.i1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.I', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357467
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1873, -1, 6348, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 74452114787817178376881809503970785874725, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 10635162896760747023547559786028911671843], 'label': '5668704.km.24.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.j1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.J', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357468
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1988, -1, 6400, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 127880141203136872883474036196720, 74452114787817178376881809503970785874725, 534484512537076226482945047212498519, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.k1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.K', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357469
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4845, -1, 7683, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 84784728159495039287519292865435141916280, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 5048696709930422514535413716, 127889352434221996633002663056068], 'label': '5668704.km.24.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.l1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.L', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357470
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 4, 'diagramx': [5085, -1, 7792, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 5048696709930422514535413716, 319116005199262768915119559171343929159108], 'label': '5668704.km.24.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.m1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.M', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357471
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '864.A', 'coset_action_label': None, 'count': 8, 'diagramx': [8644, -1, 9391, -1], 'generators': [17683942790150574222493374566644, 329449416214373286009263118061267778685384, 26976017843272882137744, 10635426027594309175760172883703132574961, 2554547201990829364, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414567549798191711522, 271353676394454377792702048198864643, 418802671169936795924582404, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.J', 'old_label': '24.n1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.N', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357472
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': [9524, -1, 9786, -1], 'generators': [74452114787817178352153793493037853330721, 17683942790150574222493374566644, 26976017843272882137744, 534484512537076226482568356043243971, 2554547201990829364, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.o1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.O', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357473
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '4.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.E', 'coset_action_label': None, 'count': 1, 'diagramx': [1349, 8608, 1020, 3010], 'generators': [339786638473518681688268813323916449252414, 26976017843272882137744, 9146650338351416526419976192144, 2554547201990829364, 295767283857029887135120785100220451842, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 244347734476267150504268574265201977478442, 376784574566547, 806582922253211364573312003], 'label': '5668704.km.4.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.E', 'subgroup_fusion': None, 'weyl_group': '5668704.km'}
    • id: 227357474
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3258, -1, 6970, -1], 'generators': [319116268330099687097478097722983425610403, 376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 340081608141416479031939002858192033822200, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716], 'label': '5668704.km.24.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.p1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.P', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357475
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3026, -1, 6866, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 74452114787817178376881809503970785874725, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 201805462074313976155119614352623181022109, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.q1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Q', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357476
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4720, -1, 7627, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 74451580294162620775276451048130883087921, 340081608141416479031939002858192033822200, 2554547201990829364, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '24.r1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.R', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357477
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 4, 'diagramx': [7158, -1, 8723, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 74451580303304641300670431646207293057923, 127880141203136872883474036196720, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 319409871296827579898741531644529159164204, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.s1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.S', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357478
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 8, 'diagramx': [6687, -1, 8511, -1], 'generators': [10635162896757390993414566838516740831429, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 340081608141416479031939002858192033822200, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 74451580285629940766273068955978649851520, 5048696709930757185768309811, 127880141203136872883474036196720], 'label': '5668704.km.24.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.J', 'old_label': '24.t1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.T', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357479
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': [732, -1, 5835, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 74451580303304641327646449112776515611524, 10635162896757390993414566838516740831429, 319415567116642468688213049675594834069240, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.u1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.U', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357480
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3373, -1, 7022, -1], 'generators': [339786375342681763505930768857197392198428, 74452114770142446820066915787232797354403, 376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 10635162896760747023547559786028911671843], 'label': '5668704.km.24.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.v1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.V', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357481
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3142, -1, 6918, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 339786375342681763505930768857197392198428, 5048696709930422514535413716, 191769431602419074701170114220486363391281, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.w1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.W', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357482
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 24, 'diagramx': [4604, -1, 7575, -1], 'generators': [74452114778675157851485011901907265849121, 17683942790150574222493374566644, 26976017843272882137744, 137981447816377065626738383066106490729333, 2554547201990829364, 10628380774572399460569719951356729305744, 339786375342681763505930768857197392198428, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.U', 'old_label': '24.x1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.X', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357483
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 4, 'diagramx': [7273, -1, 8774, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 201805198943477026950410135909632478024395, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 319116005199262768915119559171343929159108], 'label': '5668704.km.24.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.y1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Y', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357484
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '4.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '8.C', 'coset_action_label': None, 'count': 4, 'diagramx': [171, -1, 491, -1], 'generators': [10635162896757390993414566838516740831429, 9146650338351416526419976192144, 376784574566547, 10628380774572399460569719951356729305744, 806582922253211364573312003, 74452114787817178376881809503970785874725, 271353676394454377792702048198864643, 340081608141416479031939002858192033822200, 148607112713014174806923992600527462032787, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 5048696709930422514535413716, 127889352434221996633002663056068], 'label': '5668704.km.4.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '4.f1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.F', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357485
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '864.A', 'coset_action_label': None, 'count': 8, 'diagramx': [6808, -1, 8566, -1], 'generators': [84784728159495039287519292865435141916280, 17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 127880141203136872883474036196720, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 339786375342681763505930768857197392198428, 10469579123889368860499602290, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.J', 'old_label': '24.z1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Z', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357486
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 4, 'diagramx': [847, -1, 5887, -1], 'generators': [10635162896757390993414566838516740831429, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 329748986437009090077196053098679447923788, 5048696709930422514535413716, 127889352434221996633002663056068, 74452114787817178352153793493037853330721], 'label': '5668704.km.24.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.ba1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BA', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357487
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 48, 'diagramx': [4970, -1, 7740, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 137981447816377065626738383066106490729333, 295767283867499439285303609260601852214, 2554547201990829364, 74452114787817178376881809503970785874725, 127889352434221996633002663056068, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 10635162896760747023547559786028911671843], 'label': '5668704.km.24.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BB', 'old_label': '24.bb1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BB', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357488
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6337, -1, 8354, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120785100220451842, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 319116268330099687097478097722983425610403, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.bc1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357489
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2334, -1, 6555, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 74451580303304641300670431646207293057923, 295767283857029887135120785100220451842, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 10635162896760747023547559786028911671843, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.bd1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357490
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2450, -1, 6607, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 74451580303304641300670431646207293057923, 127880141203136872883474036196720, 295767283857029887135120785100220451842, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.be1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357491
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 24, 'diagramx': [9190, -1, 9636, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 74451580303304641300670431646207293057923, 295767283857029887135120785100220451842, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.bf1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357492
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7618, -1, 8930, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 74451580294162620775276451048130883087921, 2554547201990829364, 295767283857029887135120785100220451842, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.S', 'old_label': '24.bg1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BG', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357493
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 24, 'diagramx': [7503, -1, 8878, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 74451580285629940766273068955978649851520, 2554547201990829364, 295767283857029887135120785100220451842, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.U', 'old_label': '24.bh1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BH', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357494
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 4, 'diagramx': [9633, -1, 9835, -1], 'generators': [74452114787817178352153793493037853330721, 17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120073551007677585, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.bi1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BI', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357495
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '4.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '8.B', 'coset_action_label': None, 'count': 2, 'diagramx': [56, -1, 439, -1], 'generators': [10635162896757390993414566838516740831429, 9146650338351416526419976192144, 376784574566547, 10628380774572399460569719951356729305744, 806582922253211364573312003, 74452114787817178376881809503970785874725, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 5048696709930422514535413716, 295767283857029887135120785100220451842, 127889352434221996633002663056068], 'label': '5668704.km.4.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '4.g1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.G', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357496
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5879, -1, 8148, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 212140231522591230856577952399762094912829, 2554547201990829364, 295232799344492810916321487959084560784, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.bj1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BJ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357497
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6926, -1, 8619, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 74451580303304641300670431646207293057923, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 201805462074313976155119614352623181022109, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.bk1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BK', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357498
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7043, -1, 8671, -1], 'generators': [329449416214373286009263118061267778685384, 376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 340081871272253397214284729461902420464028], 'label': '5668704.km.24.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.bl1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BL', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357499
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 4, 'diagramx': [3488, -1, 7074, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 84784728159495039287519292865435141916280, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 10635162896760747023547559786028911671843, 295232799344492810916321487959084560784], 'label': '5668704.km.24.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.bm1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BM', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357500
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '864.A', 'coset_action_label': None, 'count': 8, 'diagramx': [6222, -1, 8302, -1], 'generators': [17683942790150574222493374566644, 10628380774572399460569719951356729305744, 84784728159495039287519292865435141916280, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 10635162896760747023547559786028911671843, 10469579123889368860499602290, 295232799344492810916321487959084560784], 'label': '5668704.km.24.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.J', 'old_label': '24.bn1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BN', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357501
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1642, -1, 6244, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 84784728159495039287519292865435141916280, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 127889352434221996633002663056068, 295232799344492810916321487959084560784], 'label': '5668704.km.24.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.G', 'old_label': '24.bo1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BO', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357502
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '7776.A', 'coset_action_label': None, 'count': 8, 'diagramx': [5753, -1, 8091, -1], 'generators': [10635162896757390993414567549798191711522, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 84784728159495039287519292865435141916280, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 127889352434221996633002663056068, 295232799344492810916321487959084560784], 'label': '5668704.km.24.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.J', 'old_label': '24.bp1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BP', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357503
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 2, 'diagramx': [5202, -1, 7843, -1], 'generators': [10635162896757390993414566838516740831429, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 84784728159495039287519292865435141916280, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 127889352434221996633002663056068, 295232799344492810916321487959084560784], 'label': '5668704.km.24.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.bq1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BQ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357504
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1308, -1, 6094, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 201805462074313976155119614352623181022109, 271353676394454377792702048198864643, 319116268330099687097478097722983425610403, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.br1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BR', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357505
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 8, 'diagramx': [8414, -1, 9287, -1], 'generators': [17683942790150574222493374566644, 329449416214373286009263118061267778685384, 26976017843272882137744, 20669826951063796870314538212009578583867, 2554547201990829364, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 64119773327504324015128313601500367478589, 271353676394454377792702048198864643, 418802671169936795924582404, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.J', 'old_label': '24.bs1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BS', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357506
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '4.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '8.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1118, -1, 916, -1], 'generators': [10635162896757390993414566838516740831429, 9146650338351416526419976192144, 169896969349937930797062205829531323841525, 376784574566547, 10628380774572399460569719951356729305744, 806582922253211364573312003, 84784728159495039287519292865435141916280, 271353676394454377792702048198864643, 340081608141416479031939002858192033822200, 148607112713014174806923992600527462032787, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 127889352434221996633002663056068], 'label': '5668704.km.4.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '4.h1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.H', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357507
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 4, 'diagramx': [386, -1, 5679, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 74451580294162620775276451048130883087921, 2554547201990829364, 329746007372993873509860037356728527025278, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '24.bt1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BT', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357508
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '216.A', 'coset_action_label': None, 'count': 8, 'diagramx': [155, -1, 5576, -1], 'generators': [127946784009629170692381711490250973056396, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 329451309058771694546601533467205271395883, 127889352434221996633002663056068, 10469579123889368860499602290, 20669826951056650412830333207621628499388, 84784728150966570288802176765286575446524], 'label': '5668704.km.24.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.H', 'old_label': '24.bu1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BU', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357509
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1193, -1, 6042, -1], 'generators': [329449416214373286009263118061267778685384, 127946784009629170692381711490250973056396, 376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 340081871272253397214284729461902420464028], 'label': '5668704.km.24.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.bv1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BV', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357510
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '864.A', 'coset_action_label': None, 'count': 8, 'diagramx': [8529, -1, 9339, -1], 'generators': [84784728159495039287519292865435141916280, 17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 10469579123889368860499602290, 319409608165990630694029114599540758532508, 271353676394454377792702048198864643, 418802671169936795924582404, 10635162896760747023547559786028911671843, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.J', 'old_label': '24.bw1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BW', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357511
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 2, 'diagramx': [7849, -1, 9034, -1], 'generators': [10635162896757390993414566838516740831429, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 84784728159495039287519292865435141916280, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 127889352434221996633002663056068, 340081871272253397214284729461902420464028], 'label': '5668704.km.24.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.bx1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BX', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357512
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 4, 'diagramx': [501, -1, 5731, -1], 'generators': [17683942790150574222493374566644, 84784728141815693507642186844645717635882, 26976017843272882137744, 137981447816377065626738383066106490729333, 2554547201990829364, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 319409608165990630694029114599540758532508, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.I', 'old_label': '24.by1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BY', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357513
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '7776.A', 'coset_action_label': None, 'count': 8, 'diagramx': [271, -1, 5628, -1], 'generators': [17683942790150574222493374566644, 84784728141815693507642186844645717635882, 26976017843272882137744, 137981447816377065626738383066106490729333, 2554547201990829364, 5048696709930757185768309811, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 319409608165990630694029114599540758532508, 271353676394454377792702048198864643, 418802671169936795924582404, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.K', 'old_label': '24.bz1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BZ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357514
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [963, -1, 5939, -1], 'generators': [319409871296827579898741531644529159164204, 376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 10635162896760747023547559786028911671843], 'label': '5668704.km.24.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.ca1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CA', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357515
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1078, -1, 5991, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 127880141203136872883474036196720, 534484512537076226482945047212498519, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 319409871296827579898741531644529159164204, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.cb1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CB', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357516
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1424, -1, 6146, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 295232799344492810916321487959084560784, 319116005199262768915119559171343929159108], 'label': '5668704.km.24.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.cc1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357517
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '4.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '8.E', 'coset_action_label': None, 'count': 2, 'diagramx': [633, -1, 698, -1], 'generators': [10635162896757390993414566838516740831429, 9146650338351416526419976192144, 339786375342681763505930768857197392198428, 376784574566547, 10628380774572399460569719951356729305744, 806582922253211364573312003, 74452114787817178376881809503970785874725, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 295767283857029887135120785100220451842, 127889352434221996633002663056068], 'label': '5668704.km.4.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '4.i1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.I', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357518
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7388, -1, 8826, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 340081608141416479031939002858192033822200, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 5048696709930422514535413716], 'label': '5668704.km.24.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.cd1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357519
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 4, 'diagramx': [2565, -1, 6659, -1], 'generators': [127946784009629170692381711490250973056396, 376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 340081608141416479031939002858192033822200, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 5048696709930422514535413716], 'label': '5668704.km.24.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.ce1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357520
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 8, 'diagramx': [616, -1, 5783, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 10635426027594309175760172883703132574961, 2554547201990829364, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414567549798191711522, 271353676394454377792702048198864643, 418802671169936795924582404, 202100431742821519810774806194373975396509, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.J', 'old_label': '24.cf1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357521
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': [9071, -1, 9583, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 534484512537076226482568356043243971, 2554547201990829364, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 319415567116642468688213049675594834069240, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.cg1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CG', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357522
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8298, -1, 9235, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 74452114787817178376881809503970785874725, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 10635162896760747023547559786028911671843, 295232799344492810916321487959084560784], 'label': '5668704.km.24.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.ch1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CH', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357523
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2104, -1, 6452, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 74452114787817178376881809503970785874725, 295232799344492810916321487959084560784, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.ci1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CI', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357524
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 2, 'diagramx': [4264, -1, 7423, -1], 'generators': [10635162896757390993414566838516740831429, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 127889352434221996633002663056068, 295232799344492810916321487959084560784, 74452114787817178352153793493037853330721], 'label': '5668704.km.24.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.cj1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CJ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357525
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8080, -1, 9137, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120785100220451842, 534484512537076226482945047212498519, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.ck1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CK', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357526
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2911, -1, 6814, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120785100220451842, 534484512537076226482945047212498519, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.L', 'old_label': '24.cl1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CL', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357527
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 24, 'diagramx': [2219, -1, 6503, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 244347471345430201299556277355199039648078, 2554547201990829364, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 319409871296827579898741531644529159164204, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BH', 'old_label': '24.cm1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CM', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357528
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '4.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '8.A', 'coset_action_label': None, 'count': 4, 'diagramx': [880, -1, 809, -1], 'generators': [10635162896757390993414566838516740831429, 9146650338351416526419976192144, 376784574566547, 10628380774572399460569719951356729305744, 806582922253211364573312003, 84784728159495039287519292865435141916280, 271353676394454377792702048198864643, 340081608141416479031939002858192033822200, 148607112713014174806923992600527462032787, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 5048696709930422514535413716, 127889352434221996633002663056068], 'label': '5668704.km.4.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '4.j1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.J', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357529
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4489, -1, 7523, -1], 'generators': [339786638473518681688268813323916449252414, 17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 329449153083536336804484491760033975995067, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.cn1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CN', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357530
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 12, 'diagramx': [7965, -1, 9086, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 244347471345430201299556277355199039648078, 2554547201990829364, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 319415567116642468688213049675594834069240, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.C', 'old_label': '24.co1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CO', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357531
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6004, -1, 8204, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 244347471345430201299556277355199039648078, 2554547201990829364, 127889352434221996633002663056068, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 319409871296827579898741531644529159164204, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cp1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CP', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357532
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 24, 'diagramx': [9409, -1, 9734, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 244347471345430201299556277355199039648078, 2554547201990829364, 5048696709930757185768309811, 329746007372993873509860037356728527025278, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '24.cq1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CQ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357533
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 4, 'diagramx': [9300, -1, 9685, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 10635162979475954027624187518861402908824, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 319409871296827579898741531644529159164204, 271353676394454377792702048198864643, 351327030619653574169929667130187652504394, 418802671169936795924582404, 376784574566547, 10635162896760747023547559786028911671843], 'label': '5668704.km.24.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '24.cr1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CR', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357534
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6452, -1, 8406, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 201805462074313976155119614352623181022109, 84785262644007545341310586283328022175945, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.cs1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CS', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357535
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5522, -1, 7988, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 329746007372993873509860037356728527025278, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 84785262644007545341310586283328022175945, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.ct1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CT', 'subgroup_fusion': None, 'weyl_group': '944784.pu'}
    • id: 227357536
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 12, 'diagramx': [3597, -1, 7123, -1], 'generators': [169896969349937930797062205829531323841525, 17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 319415567116642468688213049675594834069240, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.C', 'old_label': '24.cu1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CU', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357537
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5413, -1, 7939, -1], 'generators': [169896969349937930797062205829531323841525, 17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 10635162979475954027624187518861402908824, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 319409871296827579898741531644529159164204, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 10635162896760747023547559786028911671843], 'label': '5668704.km.24.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cv1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CV', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357538
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 4, 'diagramx': [8189, -1, 9186, -1], 'generators': [10635162896757390993414566838516740831429, 376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 339786638473518681688268813323916449252414, 127889352434221996633002663056068, 169896977663731296115927879316144447309274], 'label': '5668704.km.24.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.A', 'old_label': '24.cw1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CW', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357539
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '4.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '8.B', 'coset_action_label': None, 'count': 2, 'diagramx': [998, -1, 863, -1], 'generators': [10635162896757390993414566838516740831429, 9146650338351416526419976192144, 376784574566547, 10628380774572399460569719951356729305744, 806582922253211364573312003, 271353676394454377792702048198864643, 244347471345430201299556277355199039648078, 148607112713014174806923992600527462032787, 26976017843272882137744, 2554547201990829364, 534484512537076226482945047212498519, 5048696709930422514535413716, 295767283857029887135120785100220451842, 127889352434221996633002663056068], 'label': '5668704.km.4.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '4.k1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.K', 'subgroup_fusion': None, 'weyl_group': '2834352.ol'}
    • id: 227357540
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 24, 'diagramx': [6113, -1, 8253, -1], 'generators': [169896706219100981592342488567959891660804, 17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 5048696709930757185768309811, 329746007372993873509860037356728527025278, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.P', 'old_label': '24.cx1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CX', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357541
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4156, -1, 7373, -1], 'generators': [339786638473518681688268813323916449252414, 17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120785100220451842, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.cy1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CY', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357542
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.CZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2681, -1, 6711, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120785100220451842, 319114375367255915111659889580924124767838, 127889352434221996633002663056068, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.cz1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.CZ', 'subgroup_fusion': None, 'weyl_group': '944784.pu'}
    • id: 227357543
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.DA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4374, -1, 7472, -1], 'generators': [376784574566547, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 20669826758750828128195554838476720758855, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 319116005199262768915119559171343929159108, 340081871272253397214284729461902420464028], 'label': '5668704.km.24.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.da1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DA', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357544
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.DB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [6568, -1, 8458, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 74452114787817178376881809503970785874725, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 319409608165990630694029114599540758532508, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 10635162896760747023547559786028911671843, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.db1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DB', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357545
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.DC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 12, 'diagramx': [5638, -1, 8040, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 137981447816377065626738383066106490729333, 2554547201990829364, 74452114787817178376881809503970785874725, 10628380774572399460569719951356729305744, 20669826951056650412830333207621628499388, 319409608165990630694029114599540758532508, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.U', 'old_label': '24.dc1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357546
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.DD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '96.A', 'coset_action_label': None, 'count': 2, 'diagramx': [9955, -1, 9979, -1], 'generators': [10635162896757390993414566838516740831429, 17683942790150574222493374566644, 10628380774572399460569719951356729305744, 271353676394454377792702048198864643, 148607112713014174806923992600527462032787, 418802671169936795924582404, 26976017843272882137744, 2554547201990829364, 5048696709930422514535413716, 127889352434221996633002663056068, 340081871272253397214284729461902420464028, 74452114787817178352153793493037853330721], 'label': '5668704.km.24.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.C', 'old_label': '24.dd1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357547
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.DE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '288.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4040, -1, 7322, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120785100220451842, 127946784009629170692381711490250973056396, 10628380774572399460569719951356729305744, 339786375342681763505930768857197392198428, 5048696709930422514535413716, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547, 20669826758750828128195554838476720758855], 'label': '5668704.km.24.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.de1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357548
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.DF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2592.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2796, -1, 6763, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 2554547201990829364, 295767283857029887135120785100220451842, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 339786375342681763505930768857197392198428, 20669826951056650412830333207621628499388, 271353676394454377792702048198864643, 418802671169936795924582404, 376784574566547], 'label': '5668704.km.24.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.U', 'old_label': '24.df1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 227357549
      {'ambient': '5668704.km', 'aut_centralizer_order': None, 'aut_label': '24.DG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.B', 'coset_action_label': None, 'count': 6, 'diagramx': [3930, -1, 7273, -1], 'generators': [17683942790150574222493374566644, 26976017843272882137744, 244347471345430201299556277355199039648078, 2554547201990829364, 295767283857029887135120073551007677585, 127889352434221996633002663056068, 148607112713014174806923992600527462032787, 10628380774572399460569719951356729305744, 5048696709930422514535413716, 10635162896757390993414566838516740831429, 271353676394454377792702048198864643, 418802671169936795924582404], 'label': '5668704.km.24.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '24.dg1', 'projective_image': '5668704.km', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.DG', 'subgroup_fusion': None, 'weyl_group': '944784.qs'}