Formats: - HTML - YAML - JSON - 2026-07-18T17:55:22.749273
  • 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': 3, 'aut_exponent': 36, 'aut_gen_orders': [6, 18, 12, 36, 12], 'aut_gens': [[2453133561843030035820, 56419413895599613694963, 29492292052877843755615], [225488946170620856148151, 166386533424911699483123, 442243262726029960473787], [260170094713262161881741, 314071269161014010419864, 241944002959724620939501], [160864345195256638616071, 314070641708434764330785, 392703037828226241540620], [316591978764202355612281, 15794688743612040291824, 394939130696843509647757], [428790275087067945682243, 63233946789716903483504, 193513538385931809311341]], 'aut_group': None, 'aut_hash': 8246335154382275260, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5668704, 'aut_permdeg': 411, 'aut_perms': 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1549244267877895551371833063689969274031078416733543202961755510255483355362861607505341085510657804676205498083539448907385251687302950554926886663445576228049322544550367629781193179962884962637321448459429918330010705135098248006187985541641092024776842080203363357923452534941104117010781752601679754242308507587581410726559871376437230156498509356019955560414698655264161091520827363106745159450783334209258414441156011808129588166976629818416045473936906723225222947788797431400247099213640225280448612172248108729094388687163544617076385293154657959033655278649858503867459030521062014004990480003327586572206344104679427984021108831061933321272634032861524454186464398059416049689548396921035133626911093801480307787348763231111503588527638860745749279465257330349481652642670863934387503148247703480171952493413197207423742269051574777530652492485638089773173936765124736912067009902615709], 'aut_phi_ratio': 54.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 162, 1, 1], [2, 243, 1, 1], [2, 486, 1, 1], [2, 1458, 1, 1], [2, 2187, 1, 1], [3, 2, 1, 2], [3, 4, 1, 3], [3, 6, 1, 2], [3, 8, 1, 4], [3, 8, 2, 1], [3, 9, 1, 2], [3, 12, 1, 2], [3, 12, 2, 2], [3, 16, 1, 1], [3, 18, 1, 1], [3, 18, 3, 1], [3, 24, 1, 2], [3, 24, 2, 2], [3, 36, 1, 4], [3, 36, 2, 1], [3, 36, 3, 1], [3, 48, 1, 2], [3, 72, 1, 1], [3, 72, 3, 2], [3, 72, 6, 1], [3, 108, 3, 1], [3, 144, 3, 1], [3, 162, 1, 1], [3, 216, 6, 1], [3, 432, 3, 1], [3, 648, 1, 2], [4, 486, 1, 1], [4, 1458, 1, 1], [6, 12, 1, 3], [6, 12, 2, 1], [6, 18, 1, 2], [6, 18, 2, 2], [6, 24, 1, 2], [6, 24, 2, 1], [6, 36, 1, 1], [6, 36, 2, 4], [6, 54, 1, 4], [6, 54, 2, 1], [6, 72, 2, 2], [6, 81, 1, 2], [6, 108, 1, 4], [6, 108, 2, 1], [6, 108, 3, 1], [6, 108, 6, 1], [6, 162, 1, 1], [6, 162, 3, 1], [6, 216, 3, 1], [6, 216, 6, 1], [6, 243, 1, 2], [6, 324, 1, 2], [6, 324, 3, 1], [6, 324, 6, 1], [6, 486, 1, 5], [6, 648, 1, 1], [6, 648, 6, 1], [6, 972, 1, 11], [6, 972, 2, 3], [6, 972, 3, 2], [6, 1458, 1, 5], [6, 1458, 2, 3], [6, 1944, 1, 5], [6, 1944, 3, 1], [6, 2187, 1, 2], [6, 2916, 1, 6], [6, 2916, 2, 3], [6, 4374, 1, 3], [6, 5832, 1, 1], [9, 36, 3, 1], [9, 54, 1, 4], [9, 72, 6, 1], [9, 108, 1, 3], [9, 108, 3, 1], [9, 144, 3, 1], [9, 162, 1, 1], [9, 216, 1, 8], [9, 216, 2, 3], [9, 216, 6, 1], [9, 324, 1, 1], [9, 432, 1, 3], [9, 432, 3, 1], [9, 648, 1, 2], [9, 648, 2, 1], [9, 1296, 1, 1], [12, 972, 1, 1], [12, 1458, 1, 2], [12, 2916, 1, 1], [12, 2916, 3, 1], [12, 4374, 1, 2], [12, 8748, 1, 1], [18, 108, 6, 1], [18, 216, 6, 1], [18, 324, 1, 4], [18, 324, 2, 3], [18, 324, 3, 1], [18, 324, 6, 1], [18, 486, 1, 4], [18, 648, 1, 4], [18, 648, 2, 3], [18, 648, 6, 1], [18, 972, 1, 4], [18, 972, 2, 1], [18, 972, 3, 1], [18, 1458, 1, 1], [18, 1944, 1, 1], [18, 1944, 2, 1], [18, 2916, 1, 6], [18, 5832, 1, 5], [36, 8748, 1, 5]], 'aut_supersolvable': False, 'aut_tex': 'C_3^6.C_3^3.C_6^2.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': None, 'autcentquo_hash': 8246335154382275260, 'autcentquo_nilpotent': False, 'autcentquo_order': 5668704, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^6.C_3^3.C_6^2.C_2^3', 'cc_stats': [[1, 1, 1], [2, 6, 1], [2, 9, 1], [2, 162, 1], [2, 243, 1], [2, 486, 1], [2, 1458, 1], [2, 2187, 1], [3, 2, 2], [3, 4, 3], [3, 6, 2], [3, 8, 6], [3, 9, 2], [3, 12, 6], [3, 16, 1], [3, 18, 4], [3, 24, 6], [3, 36, 9], [3, 48, 2], [3, 72, 13], [3, 108, 3], [3, 144, 3], [3, 162, 1], [3, 216, 6], [3, 432, 3], [3, 648, 2], [4, 486, 1], [4, 1458, 1], [6, 12, 5], [6, 18, 6], [6, 24, 4], [6, 36, 9], [6, 54, 6], [6, 72, 4], [6, 81, 2], [6, 108, 15], [6, 162, 4], [6, 216, 9], [6, 243, 2], [6, 324, 11], [6, 486, 5], [6, 648, 7], [6, 972, 23], [6, 1458, 11], [6, 1944, 8], [6, 2187, 2], [6, 2916, 12], [6, 4374, 3], [6, 5832, 1], [9, 36, 3], [9, 54, 4], [9, 72, 6], [9, 108, 6], [9, 144, 3], [9, 162, 1], [9, 216, 20], [9, 324, 1], [9, 432, 6], [9, 648, 4], [9, 1296, 1], [12, 972, 1], [12, 1458, 2], [12, 2916, 4], [12, 4374, 2], [12, 8748, 1], [18, 108, 6], [18, 216, 6], [18, 324, 19], [18, 486, 4], [18, 648, 16], [18, 972, 9], [18, 1458, 1], [18, 1944, 3], [18, 2916, 6], [18, 5832, 5], [36, 8748, 5]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '314928.nv', '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', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 360, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 162, 1, 1], [2, 243, 1, 1], [2, 486, 1, 1], [2, 1458, 1, 1], [2, 2187, 1, 1], [3, 2, 1, 2], [3, 4, 1, 3], [3, 6, 2, 1], [3, 8, 1, 6], [3, 9, 2, 1], [3, 12, 2, 3], [3, 16, 1, 1], [3, 18, 1, 4], [3, 24, 2, 3], [3, 36, 1, 3], [3, 36, 2, 3], [3, 48, 2, 1], [3, 72, 1, 13], [3, 108, 1, 3], [3, 144, 1, 3], [3, 162, 1, 1], [3, 216, 1, 6], [3, 432, 1, 3], [3, 648, 1, 2], [4, 486, 1, 1], [4, 1458, 1, 1], [6, 12, 1, 5], [6, 18, 1, 2], [6, 18, 2, 2], [6, 24, 1, 4], [6, 36, 1, 1], [6, 36, 2, 4], [6, 54, 2, 3], [6, 72, 2, 2], [6, 81, 2, 1], [6, 108, 1, 9], [6, 108, 2, 3], [6, 162, 1, 4], [6, 216, 1, 9], [6, 243, 2, 1], [6, 324, 1, 11], [6, 486, 1, 1], [6, 486, 2, 2], [6, 648, 1, 7], [6, 972, 1, 11], [6, 972, 2, 6], [6, 1458, 1, 1], [6, 1458, 2, 5], [6, 1944, 1, 6], [6, 1944, 2, 1], [6, 2187, 2, 1], [6, 2916, 1, 2], [6, 2916, 2, 5], [6, 4374, 1, 1], [6, 4374, 2, 1], [6, 5832, 1, 1], [9, 36, 1, 3], [9, 54, 1, 2], [9, 54, 2, 1], [9, 72, 1, 6], [9, 108, 1, 4], [9, 108, 2, 1], [9, 144, 1, 3], [9, 162, 1, 1], [9, 216, 1, 10], [9, 216, 2, 5], [9, 324, 1, 1], [9, 432, 1, 4], [9, 432, 2, 1], [9, 648, 1, 4], [9, 1296, 1, 1], [12, 972, 1, 1], [12, 1458, 2, 1], [12, 2916, 1, 4], [12, 4374, 2, 1], [12, 8748, 1, 1], [18, 108, 1, 6], [18, 216, 1, 6], [18, 324, 1, 11], [18, 324, 2, 4], [18, 486, 1, 2], [18, 486, 2, 1], [18, 648, 1, 8], [18, 648, 2, 4], [18, 972, 1, 7], [18, 972, 2, 1], [18, 1458, 1, 1], [18, 1944, 1, 3], [18, 2916, 1, 4], [18, 2916, 2, 1], [18, 5832, 1, 3], [18, 5832, 2, 1], [36, 8748, 1, 3], [36, 8748, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [9, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 36], [48, 1, 9], [72, 0, 8], [144, 0, 2]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '3888.iv', 'hash': 5902825399310417443, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [6, 18, 18], 'inner_gens': [[2453133561843030035820, 168622748534422662646905, 94488076604791766055979], [168737978037908180568295, 56419413895599613694963, 235121383449727860960397], [312078862223786958814483, 110768711018619232092065, 29492292052877843755615]], 'inner_hash': 5902825399310417443, 'inner_nilpotent': False, 'inner_order': 314928, 'inner_split': None, 'inner_tex': 'C_3^7.D_6:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 22], [3, 16], [4, 29], [6, 36], [8, 36], [12, 90], [16, 4], [18, 16], [24, 62], [36, 16], [48, 12], [72, 28], [144, 3]], 'label': '314928.nv', '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.D6:D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 237, 'number_characteristic_subgroups': 118, 'number_conjugacy_classes': 378, 'number_divisions': 306, 'number_normal_subgroups': 118, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 314928, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 4551], [3, 6560], [4, 1944], [6, 128856], [9, 13122], [12, 33048], [18, 83106], [36, 43740]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [3, 6], 'outer_gen_pows': [449016840019590703706550, 161856655413382095667200], 'outer_gens': [[168737978037908180568361, 105151133900289405237473, 348110243924033400329899], [18262406595680955515191, 311813049578517644734744, 36296958592010863681335]], 'outer_group': '18.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 18, 'outer_permdeg': 18, 'outer_perms': [3378942629719957, 2386194864116280], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times C_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 22], [4, 29], [6, 12], [8, 36], [12, 54], [16, 4], [18, 16], [24, 64], [36, 8], [48, 22], [72, 24], [96, 1], [144, 5], [288, 1]], 'representations': {'PC': {'code': '24538067914315831980504839417288933641760499969173279440472023756586213279685606194822613855276881525987115782085512097765754151126848019876977298197516884263537513734998253998080335581393343660017123703690640809418159325789572754199733869587608133545802656583597301300722949225290524805792099424253281481525185921394783994948369543642353662618297755323600087176566065468449188120645985663', 'gens': [1, 2, 4, 6, 8, 9, 10, 11, 12], 'pres': [13, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3382704, 4594149, 66, 11906234, 1968436, 8770323, 5402920, 3456209, 146, 5999764, 7376477, 276150, 20189525, 3705174, 5069875, 687536, 11991, 226, 18214566, 11688787, 6984464, 28437, 404644, 132762, 5181703, 9824276, 6735489, 1832110, 920459, 156072, 152029, 50642, 303272, 6916125, 25319, 4285, 36791049, 13079062, 2187155, 2574048, 861961, 554654, 45717, 78490, 7146, 11963962, 10007735, 2630664, 1570189, 81572, 28389, 38711, 2701, 2714, 42164939, 13927704, 5144293, 2145362, 1615599, 533596, 151721, 11828, 2013, 622, 35481900, 17740969]}, 'Perm': {'d': 24, 'gens': [2453133561843030035820, 56419413895599613694963, 29492292052877843755615]}}, 'schur_multiplier': [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': 48, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^7.D_6:D_6', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    Showing the first 100 of 378 matching records in this table.
    • id: 158356440
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 360, 'group_order': 314928, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 158356551
      {'aut_label': '2A', 'centralizer': '6.F', 'counter': 2, 'group_counter': 360, 'group_order': 314928, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 598, 'size': 6}
    • id: 158356662
      {'aut_label': '2B', 'centralizer': '9.A', 'counter': 3, 'group_counter': 360, 'group_order': 314928, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 55, 'size': 9}
    • id: 158356752
      {'aut_label': '2C', 'centralizer': None, 'counter': 4, 'group_counter': 360, 'group_order': 314928, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 25903998727064654031414, 'size': 162}
    • id: 158356763
      {'aut_label': '2D', 'centralizer': None, 'counter': 5, 'group_counter': 360, 'group_order': 314928, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 215631954729750988800, 'size': 243}
    • id: 158356774
      {'aut_label': '2E', 'centralizer': None, 'counter': 6, 'group_counter': 360, 'group_order': 314928, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 289447413892038957945601, 'size': 486}
    • id: 158356785
      {'aut_label': '2F', 'centralizer': None, 'counter': 7, 'group_counter': 360, 'group_order': 314928, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 11521276934226303243539, 'size': 1458}
    • id: 158356796
      {'aut_label': '2G', 'centralizer': None, 'counter': 8, 'group_counter': 360, 'group_order': 314928, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 121771685486335183452861, 'size': 2187}
    • id: 158356807
      {'aut_label': '3A', 'centralizer': '2.A', 'counter': 9, 'group_counter': 360, 'group_order': 314928, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 54167378773480723255680, 'size': 2}
    • id: 158356441
      {'aut_label': '3B', 'centralizer': '2.C', 'counter': 10, 'group_counter': 360, 'group_order': 314928, 'label': '3B', 'order': 3, 'powers': [10, 1], 'representative': 158494346778656384294400, 'size': 2}
    • id: 158356452
      {'aut_label': '3C', 'centralizer': '4.H', 'counter': 11, 'group_counter': 360, 'group_order': 314928, 'label': '3C', 'order': 3, 'powers': [11, 1], 'representative': 181, 'size': 4}
    • id: 158356463
      {'aut_label': '3D', 'centralizer': '4.J', 'counter': 12, 'group_counter': 360, 'group_order': 314928, 'label': '3D', 'order': 3, 'powers': [12, 1], 'representative': 20, 'size': 4}
    • id: 158356474
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    • id: 158356485
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    • id: 158356496
      {'aut_label': '3F-1', 'centralizer': '6.H', 'counter': 15, 'group_counter': 360, 'group_order': 314928, 'label': '3F-1', 'order': 3, 'powers': [14, 1], 'representative': 25987943544116400, 'size': 6}
    • id: 158356507
      {'aut_label': '3G', 'centralizer': '8.D', 'counter': 16, 'group_counter': 360, 'group_order': 314928, 'label': '3G', 'order': 3, 'powers': [16, 1], 'representative': 6795281690365111297381, 'size': 8}
    • id: 158356518
      {'aut_label': '3G', 'centralizer': '8.D', 'counter': 17, 'group_counter': 360, 'group_order': 314928, 'label': '3H', 'order': 3, 'powers': [17, 1], 'representative': 6795281690365111297386, 'size': 8}
    • id: 158356529
      {'aut_label': '3I', 'centralizer': '8.D', 'counter': 18, 'group_counter': 360, 'group_order': 314928, 'label': '3I', 'order': 3, 'powers': [18, 1], 'representative': 161856655413382095667381, 'size': 8}
    • id: 158356540
      {'aut_label': '3J', 'centralizer': '8.D', 'counter': 19, 'group_counter': 360, 'group_order': 314928, 'label': '3J', 'order': 3, 'powers': [19, 1], 'representative': 158494346778656384294581, 'size': 8}
    • id: 158356552
      {'aut_label': '3K', 'centralizer': '8.F', 'counter': 20, 'group_counter': 360, 'group_order': 314928, 'label': '3K', 'order': 3, 'powers': [20, 1], 'representative': 58707205932083320286655, 'size': 8}
    • id: 158356563
      {'aut_label': '3L', 'centralizer': '8.E', 'counter': 21, 'group_counter': 360, 'group_order': 314928, 'label': '3L', 'order': 3, 'powers': [21, 1], 'representative': 161856655413382095667220, 'size': 8}
    • id: 158356574
      {'aut_label': '3M1', 'centralizer': '9.C', 'counter': 22, 'group_counter': 360, 'group_order': 314928, 'label': '3M1', 'order': 3, 'powers': [23, 1], 'representative': 1281227989574131200, 'size': 9}
    • id: 158356585
      {'aut_label': '3M-1', 'centralizer': '9.C', 'counter': 23, 'group_counter': 360, 'group_order': 314928, 'label': '3M-1', 'order': 3, 'powers': [22, 1], 'representative': 512951525861649840, 'size': 9}
    • id: 158356596
      {'aut_label': '3N1', 'centralizer': '12.R', 'counter': 24, 'group_counter': 360, 'group_order': 314928, 'label': '3N1', 'order': 3, 'powers': [25, 1], 'representative': 64401664134855781, 'size': 12}
    • id: 158356607
      {'aut_label': '3N-1', 'centralizer': '12.R', 'counter': 25, 'group_counter': 360, 'group_order': 314928, 'label': '3N-1', 'order': 3, 'powers': [24, 1], 'representative': 25987943544116778, 'size': 12}
    • id: 158356618
      {'aut_label': '3N1', 'centralizer': '12.R', 'counter': 26, 'group_counter': 360, 'group_order': 314928, 'label': '3O1', 'order': 3, 'powers': [27, 1], 'representative': 64401664134855786, 'size': 12}
    • id: 158356629
      {'aut_label': '3N-1', 'centralizer': '12.R', 'counter': 27, 'group_counter': 360, 'group_order': 314928, 'label': '3O-1', 'order': 3, 'powers': [26, 1], 'representative': 25987943544116773, 'size': 12}
    • id: 158356640
      {'aut_label': '3P1', 'centralizer': '12.BV', 'counter': 28, 'group_counter': 360, 'group_order': 314928, 'label': '3P1', 'order': 3, 'powers': [29, 1], 'representative': 6796376850667783680000, 'size': 12}
    • id: 158356651
      {'aut_label': '3P-1', 'centralizer': '12.BV', 'counter': 29, 'group_counter': 360, 'group_order': 314928, 'label': '3P-1', 'order': 3, 'powers': [28, 1], 'representative': 2309337271127813068800, 'size': 12}
    • id: 158356663
      {'aut_label': '3Q', 'centralizer': '16.a1', 'counter': 30, 'group_counter': 360, 'group_order': 314928, 'label': '3Q', 'order': 3, 'powers': [30, 1], 'representative': 2308971973569648634815, 'size': 16}
    • id: 158356674
      {'aut_label': '3R', 'centralizer': '18.X', 'counter': 31, 'group_counter': 360, 'group_order': 314928, 'label': '3R', 'order': 3, 'powers': [31, 1], 'representative': 1249216643121310080, 'size': 18}
    • id: 158356685
      {'aut_label': '3S', 'centralizer': '18.O', 'counter': 32, 'group_counter': 360, 'group_order': 314928, 'label': '3S', 'order': 3, 'powers': [32, 1], 'representative': 40236940800, 'size': 18}
    • id: 158356696
      {'aut_label': '3S', 'centralizer': '18.O', 'counter': 33, 'group_counter': 360, 'group_order': 314928, 'label': '3T', 'order': 3, 'powers': [33, 1], 'representative': 1249216656446263680, 'size': 18}
    • id: 158356707
      {'aut_label': '3S', 'centralizer': '18.O', 'counter': 34, 'group_counter': 360, 'group_order': 314928, 'label': '3U', 'order': 3, 'powers': [34, 1], 'representative': 161857385274744644083200, 'size': 18}
    • id: 158356718
      {'aut_label': '3V1', 'centralizer': '24.Q', 'counter': 35, 'group_counter': 360, 'group_order': 314928, 'label': '3V1', 'order': 3, 'powers': [36, 1], 'representative': 6796376850667783680181, 'size': 24}
    • id: 158356729
      {'aut_label': '3V-1', 'centralizer': '24.Q', 'counter': 36, 'group_counter': 360, 'group_order': 314928, 'label': '3V-1', 'order': 3, 'powers': [35, 1], 'representative': 2309337271127813069178, 'size': 24}
    • id: 158356740
      {'aut_label': '3V1', 'centralizer': '24.Q', 'counter': 37, 'group_counter': 360, 'group_order': 314928, 'label': '3W1', 'order': 3, 'powers': [38, 1], 'representative': 6796376850667783680186, 'size': 24}
    • id: 158356750
      {'aut_label': '3V-1', 'centralizer': '24.Q', 'counter': 38, 'group_counter': 360, 'group_order': 314928, 'label': '3W-1', 'order': 3, 'powers': [37, 1], 'representative': 2309337271127813069173, 'size': 24}
    • id: 158356751
      {'aut_label': '3X1', 'centralizer': '24.BR', 'counter': 39, 'group_counter': 360, 'group_order': 314928, 'label': '3X1', 'order': 3, 'powers': [40, 1], 'representative': 25987943544116766, 'size': 24}
    • id: 158356753
      {'aut_label': '3X-1', 'centralizer': '24.BR', 'counter': 40, 'group_counter': 360, 'group_order': 314928, 'label': '3X-1', 'order': 3, 'powers': [39, 1], 'representative': 64401664134855774, 'size': 24}
    • id: 158356754
      {'aut_label': '3Y', 'centralizer': '36.A', 'counter': 41, 'group_counter': 360, 'group_order': 314928, 'label': '3Y', 'order': 3, 'powers': [41, 1], 'representative': 64401694283288880, 'size': 36}
    • id: 158356755
      {'aut_label': '3Y', 'centralizer': '36.A', 'counter': 42, 'group_counter': 360, 'group_order': 314928, 'label': '3Z', 'order': 3, 'powers': [42, 1], 'representative': 6795281690379115194240, 'size': 36}
    • id: 158356756
      {'aut_label': '3Y', 'centralizer': '36.A', 'counter': 43, 'group_counter': 360, 'group_order': 314928, 'label': '3AA', 'order': 3, 'powers': [43, 1], 'representative': 6796376850681108633600, 'size': 36}
    • id: 158356757
      {'aut_label': '3AB1', 'centralizer': '36.BL', 'counter': 44, 'group_counter': 360, 'group_order': 314928, 'label': '3AB1', 'order': 3, 'powers': [45, 1], 'representative': 1281227989574131381, 'size': 36}
    • id: 158356758
      {'aut_label': '3AB-1', 'centralizer': '36.BL', 'counter': 45, 'group_counter': 360, 'group_order': 314928, 'label': '3AB-1', 'order': 3, 'powers': [44, 1], 'representative': 512951525861650218, 'size': 36}
    • id: 158356759
      {'aut_label': '3AC1', 'centralizer': '36.BL', 'counter': 46, 'group_counter': 360, 'group_order': 314928, 'label': '3AC1', 'order': 3, 'powers': [47, 1], 'representative': 1249216643121310261, 'size': 36}
    • id: 158356760
      {'aut_label': '3AC1', 'centralizer': '36.BL', 'counter': 47, 'group_counter': 360, 'group_order': 314928, 'label': '3AC-1', 'order': 3, 'powers': [46, 1], 'representative': 551366640350669178, 'size': 36}
    • id: 158356761
      {'aut_label': '3AD1', 'centralizer': '36.MJ', 'counter': 48, 'group_counter': 360, 'group_order': 314928, 'label': '3AD1', 'order': 3, 'powers': [49, 1], 'representative': 158494090675349861112255, 'size': 36}
    • id: 158356762
      {'aut_label': '3AD-1', 'centralizer': '36.MJ', 'counter': 49, 'group_counter': 360, 'group_order': 314928, 'label': '3AD-1', 'order': 3, 'powers': [48, 1], 'representative': 58706181552266084390420, 'size': 36}
    • id: 158356764
      {'aut_label': '3AE1', 'centralizer': '48.P', 'counter': 50, 'group_counter': 360, 'group_order': 314928, 'label': '3AE1', 'order': 3, 'powers': [51, 1], 'representative': 2309337271127813068815, 'size': 48}
    • id: 158356765
      {'aut_label': '3AE-1', 'centralizer': '48.P', 'counter': 51, 'group_counter': 360, 'group_order': 314928, 'label': '3AE-1', 'order': 3, 'powers': [50, 1], 'representative': 2310073536245595281295, 'size': 48}
    • id: 158356766
      {'aut_label': '3AF', 'centralizer': None, 'counter': 52, 'group_counter': 360, 'group_order': 314928, 'label': '3AF', 'order': 3, 'powers': [52, 1], 'representative': 40236940981, 'size': 72}
    • id: 158356767
      {'aut_label': '3AG', 'centralizer': None, 'counter': 53, 'group_counter': 360, 'group_order': 314928, 'label': '3AG', 'order': 3, 'powers': [53, 1], 'representative': 64401694283289061, 'size': 72}
    • id: 158356768
      {'aut_label': '3AG', 'centralizer': None, 'counter': 54, 'group_counter': 360, 'group_order': 314928, 'label': '3AH', 'order': 3, 'powers': [54, 1], 'representative': 64401694283289066, 'size': 72}
    • id: 158356769
      {'aut_label': '3AF', 'centralizer': None, 'counter': 55, 'group_counter': 360, 'group_order': 314928, 'label': '3AI', 'order': 3, 'powers': [55, 1], 'representative': 1249216656446263861, 'size': 72}
    • id: 158356770
      {'aut_label': '3AG', 'centralizer': None, 'counter': 56, 'group_counter': 360, 'group_order': 314928, 'label': '3AJ', 'order': 3, 'powers': [56, 1], 'representative': 6795281690379115194421, 'size': 72}
    • id: 158356771
      {'aut_label': '3AG', 'centralizer': None, 'counter': 57, 'group_counter': 360, 'group_order': 314928, 'label': '3AK', 'order': 3, 'powers': [57, 1], 'representative': 6795281690379115194426, 'size': 72}
    • id: 158356772
      {'aut_label': '3AG', 'centralizer': None, 'counter': 58, 'group_counter': 360, 'group_order': 314928, 'label': '3AL', 'order': 3, 'powers': [58, 1], 'representative': 6796376850681108633781, 'size': 72}
    • id: 158356773
      {'aut_label': '3AG', 'centralizer': None, 'counter': 59, 'group_counter': 360, 'group_order': 314928, 'label': '3AM', 'order': 3, 'powers': [59, 1], 'representative': 6796376850681108633786, 'size': 72}
    • id: 158356775
      {'aut_label': '3AF', 'centralizer': None, 'counter': 60, 'group_counter': 360, 'group_order': 314928, 'label': '3AN', 'order': 3, 'powers': [60, 1], 'representative': 161857385274744644083381, 'size': 72}
    • id: 158356776
      {'aut_label': '3AO', 'centralizer': None, 'counter': 61, 'group_counter': 360, 'group_order': 314928, 'label': '3AO', 'order': 3, 'powers': [61, 1], 'representative': 161856412115240861948334, 'size': 72}
    • id: 158356777
      {'aut_label': '3AO', 'centralizer': None, 'counter': 62, 'group_counter': 360, 'group_order': 314928, 'label': '3AP', 'order': 3, 'powers': [62, 1], 'representative': 6795223712011994918766, 'size': 72}
    • id: 158356778
      {'aut_label': '3AQ', 'centralizer': None, 'counter': 63, 'group_counter': 360, 'group_order': 314928, 'label': '3AQ', 'order': 3, 'powers': [63, 1], 'representative': 58706194358848514607534, 'size': 72}
    • id: 158356779
      {'aut_label': '3AO', 'centralizer': None, 'counter': 64, 'group_counter': 360, 'group_order': 314928, 'label': '3AR', 'order': 3, 'powers': [64, 1], 'representative': 54167410784813851123566, 'size': 72}
    • id: 158356780
      {'aut_label': '3AS', 'centralizer': None, 'counter': 65, 'group_counter': 360, 'group_order': 314928, 'label': '3AS', 'order': 3, 'powers': [65, 1], 'representative': 11325403000045608652080, 'size': 108}
    • id: 158356781
      {'aut_label': '3AS', 'centralizer': None, 'counter': 66, 'group_counter': 360, 'group_order': 314928, 'label': '3AT', 'order': 3, 'powers': [66, 1], 'representative': 11326498179962757891120, 'size': 108}
    • id: 158356782
      {'aut_label': '3AS', 'centralizer': None, 'counter': 67, 'group_counter': 360, 'group_order': 314928, 'label': '3AU', 'order': 3, 'powers': [67, 1], 'representative': 166387506604026249795120, 'size': 108}
    • id: 158356783
      {'aut_label': '3AV', 'centralizer': '144.A', 'counter': 68, 'group_counter': 360, 'group_order': 314928, 'label': '3AV', 'order': 3, 'powers': [68, 1], 'representative': 25987957548013455, 'size': 144}
    • id: 158356784
      {'aut_label': '3AV', 'centralizer': '144.A', 'counter': 69, 'group_counter': 360, 'group_order': 314928, 'label': '3AW', 'order': 3, 'powers': [69, 1], 'representative': 2308971973599797068095, 'size': 144}
    • id: 158356786
      {'aut_label': '3AV', 'centralizer': '144.A', 'counter': 70, 'group_counter': 360, 'group_order': 314928, 'label': '3AX', 'order': 3, 'powers': [70, 1], 'representative': 2309337271114488115215, 'size': 144}
    • id: 158356787
      {'aut_label': '3AY', 'centralizer': None, 'counter': 71, 'group_counter': 360, 'group_order': 314928, 'label': '3AY', 'order': 3, 'powers': [71, 1], 'representative': 320830011876885931612080, 'size': 162}
    • id: 158356788
      {'aut_label': '3AZ', 'centralizer': None, 'counter': 72, 'group_counter': 360, 'group_order': 314928, 'label': '3AZ', 'order': 3, 'powers': [72, 1], 'representative': 11326498179962757891493, 'size': 216}
    • id: 158356789
      {'aut_label': '3AZ', 'centralizer': None, 'counter': 73, 'group_counter': 360, 'group_order': 314928, 'label': '3BA', 'order': 3, 'powers': [73, 1], 'representative': 208099018859814147703866, 'size': 216}
    • id: 158356790
      {'aut_label': '3AZ', 'centralizer': None, 'counter': 74, 'group_counter': 360, 'group_order': 314928, 'label': '3BB', 'order': 3, 'powers': [74, 1], 'representative': 13561265973512949234853, 'size': 216}
    • id: 158356791
      {'aut_label': '3AZ', 'centralizer': None, 'counter': 75, 'group_counter': 360, 'group_order': 314928, 'label': '3BC', 'order': 3, 'powers': [75, 1], 'representative': 160747105361505728048298, 'size': 216}
    • id: 158356792
      {'aut_label': '3AZ', 'centralizer': None, 'counter': 76, 'group_counter': 360, 'group_order': 314928, 'label': '3BD', 'order': 3, 'powers': [76, 1], 'representative': 365673630463237534596858, 'size': 216}
    • id: 158356793
      {'aut_label': '3AZ', 'centralizer': None, 'counter': 77, 'group_counter': 360, 'group_order': 314928, 'label': '3BE', 'order': 3, 'powers': [77, 1], 'representative': 370157808206247656999413, 'size': 216}
    • id: 158356794
      {'aut_label': '3BF', 'centralizer': None, 'counter': 78, 'group_counter': 360, 'group_order': 314928, 'label': '3BF', 'order': 3, 'powers': [78, 1], 'representative': 4561973853195550543935, 'size': 432}
    • id: 158356795
      {'aut_label': '3BF', 'centralizer': None, 'counter': 79, 'group_counter': 360, 'group_order': 314928, 'label': '3BG', 'order': 3, 'powers': [79, 1], 'representative': 4562339149402571219775, 'size': 432}
    • id: 158356797
      {'aut_label': '3BF', 'centralizer': None, 'counter': 80, 'group_counter': 360, 'group_order': 314928, 'label': '3BH', 'order': 3, 'powers': [80, 1], 'representative': 56419644386637742739775, 'size': 432}
    • id: 158356798
      {'aut_label': '3BI', 'centralizer': None, 'counter': 81, 'group_counter': 360, 'group_order': 314928, 'label': '3BI', 'order': 3, 'powers': [81, 1], 'representative': 320829518870729038603455, 'size': 648}
    • id: 158356799
      {'aut_label': '3BJ', 'centralizer': None, 'counter': 82, 'group_counter': 360, 'group_order': 314928, 'label': '3BJ', 'order': 3, 'powers': [82, 1], 'representative': 264874987323280133458021, 'size': 648}
    • id: 158356800
      {'aut_label': '4A', 'centralizer': None, 'counter': 83, 'group_counter': 360, 'group_order': 314928, 'label': '4A', 'order': 4, 'powers': [3, 83], 'representative': 297527522188155207747652, 'size': 486}
    • id: 158356801
      {'aut_label': '4B', 'centralizer': None, 'counter': 84, 'group_counter': 360, 'group_order': 314928, 'label': '4B', 'order': 4, 'powers': [3, 84], 'representative': 401761327758365427431357, 'size': 1458}
    • id: 158356802
      {'aut_label': '6A', 'centralizer': '12.P', 'counter': 85, 'group_counter': 360, 'group_order': 314928, 'label': '6A', 'order': 6, 'powers': [11, 2], 'representative': 323, 'size': 12}
    • id: 158356803
      {'aut_label': '6B', 'centralizer': '12.BU', 'counter': 86, 'group_counter': 360, 'group_order': 314928, 'label': '6B', 'order': 6, 'powers': [13, 2], 'representative': 6795281690365111297516, 'size': 12}
    • id: 158356804
      {'aut_label': '6B', 'centralizer': '12.BU', 'counter': 87, 'group_counter': 360, 'group_order': 314928, 'label': '6C', 'order': 6, 'powers': [13, 2], 'representative': 6795281690365111297541, 'size': 12}
    • id: 158356805
      {'aut_label': '6D', 'centralizer': '12.BU', 'counter': 88, 'group_counter': 360, 'group_order': 314928, 'label': '6D', 'order': 6, 'powers': [10, 2], 'representative': 58707205932083320286956, 'size': 12}
    • id: 158356806
      {'aut_label': '6E', 'centralizer': '12.BU', 'counter': 89, 'group_counter': 360, 'group_order': 314928, 'label': '6E', 'order': 6, 'powers': [9, 2], 'representative': 54167378773480723255996, 'size': 12}
    • id: 158356808
      {'aut_label': '6F', 'centralizer': '18.D', 'counter': 90, 'group_counter': 360, 'group_order': 314928, 'label': '6F', 'order': 6, 'powers': [10, 3], 'representative': 58707205932083320286774, 'size': 18}
    • id: 158356809
      {'aut_label': '6G', 'centralizer': '18.B', 'counter': 91, 'group_counter': 360, 'group_order': 314928, 'label': '6G', 'order': 6, 'powers': [9, 3], 'representative': 54167378773480723256076, 'size': 18}
    • id: 158356810
      {'aut_label': '6H1', 'centralizer': '18.E', 'counter': 92, 'group_counter': 360, 'group_order': 314928, 'label': '6H1', 'order': 6, 'powers': [14, 2], 'representative': 25987943544116716, 'size': 18}
    • id: 158356811
      {'aut_label': '6H-1', 'centralizer': '18.E', 'counter': 93, 'group_counter': 360, 'group_order': 314928, 'label': '6H-1', 'order': 6, 'powers': [15, 2], 'representative': 64401664134855916, 'size': 18}
    • id: 158356812
      {'aut_label': '6H1', 'centralizer': '18.E', 'counter': 94, 'group_counter': 360, 'group_order': 314928, 'label': '6I1', 'order': 6, 'powers': [14, 2], 'representative': 25987943544116741, 'size': 18}
    • id: 158356813
      {'aut_label': '6H-1', 'centralizer': '18.E', 'counter': 95, 'group_counter': 360, 'group_order': 314928, 'label': '6I-1', 'order': 6, 'powers': [15, 2], 'representative': 64401664134855941, 'size': 18}
    • id: 158356814
      {'aut_label': '6J', 'centralizer': '24.F', 'counter': 96, 'group_counter': 360, 'group_order': 314928, 'label': '6J', 'order': 6, 'powers': [16, 2], 'representative': 2308971973569648635123, 'size': 24}
    • id: 158356815
      {'aut_label': '6J', 'centralizer': '24.F', 'counter': 97, 'group_counter': 360, 'group_order': 314928, 'label': '6K', 'order': 6, 'powers': [17, 2], 'representative': 2308971973569648635146, 'size': 24}
    • id: 158356816
      {'aut_label': '6L', 'centralizer': '24.F', 'counter': 98, 'group_counter': 360, 'group_order': 314928, 'label': '6L', 'order': 6, 'powers': [18, 2], 'representative': 54167378773480723256003, 'size': 24}
    • id: 158356817
      {'aut_label': '6M', 'centralizer': '24.F', 'counter': 99, 'group_counter': 360, 'group_order': 314928, 'label': '6M', 'order': 6, 'powers': [19, 2], 'representative': 58707205932083320286963, 'size': 24}
    • id: 158356442
      {'aut_label': '6N', 'centralizer': '36.BK', 'counter': 100, 'group_counter': 360, 'group_order': 314928, 'label': '6N', 'order': 6, 'powers': [13, 3], 'representative': 6795281690365111297255, 'size': 36}
  • group 314928.nv does not appear in gps_qchar
  • group 314928.nv does not appear in gps_char
  • gps_subgroup_search • Show schema
    Showing the first 100 of 915 matching records in this table.
    • id: 187011898
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 314928, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '314928.nv.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': '314928.nv', 'subgroup_hash': 5902825399310417443, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^7.D_6:D_6', 'supersolvable': False, 'sylow': 0}
    • id: 187012009
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 157464, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': '157464.ox', 'subgroup_hash': 208150519196721419, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^5.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012120
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 157464, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1651865077919200556, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^7.C_6^2.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 187012231
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 157464, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.ov', 'subgroup_hash': 4826892033351301324, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^5.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012342
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 157464, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': '157464.ll', 'subgroup_hash': 6447292394418039885, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012453
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 157464, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': '157464.mj', 'subgroup_hash': 2548624222297213438, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^4.C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 187012564
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 157464, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.2.F', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1', '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': '157464.nb', 'subgroup_hash': 5753077851595127159, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.(C_6.S_3^2)', 'supersolvable': False, 'sylow': 0}
    • id: 187012675
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 157464, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.2.G', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1', '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': '157464.mh', 'subgroup_hash': 873396872267622553, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^4.C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 187012786
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 52488, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.3.A', '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': '104976.ie', 'subgroup_hash': 646165495038383972, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^7.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 187011899
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 52488, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.3.B', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '104976.id', 'subgroup_hash': 7971494032866542798, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^7.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 187011910
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 52488, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.3.C', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '104976.nv', 'subgroup_hash': 2786092589205405714, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.D_6:D_6', 'supersolvable': False, 'sylow': 0}
    • id: 187011921
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 52488, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.3.D', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.nw', 'subgroup_hash': 2290664300897465572, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.D_6:D_6', 'supersolvable': False, 'sylow': 0}
    • id: 187011932
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 52488, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.3.E', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.nu', 'subgroup_hash': 8228577617214533321, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.D_6:D_6', 'supersolvable': False, 'sylow': 0}
    • id: 187011943
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 78732, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1722648214006327155, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 187011954
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 78732, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.iq', 'subgroup_hash': 8148641648721072420, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.(C_3\\times S_3^2)', 'supersolvable': True, 'sylow': 0}
    • id: 187011965
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 78732, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': None, 'subgroup_hash': 6299221875271814386, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.C_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 187011976
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 78732, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': '78732.iw', 'subgroup_hash': 7675179532199776528, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 187011987
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 78732, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': None, 'subgroup_hash': 403171074063134179, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.C_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 187011998
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 78732, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.4.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', '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': '78732.jk', 'subgroup_hash': 8614154423771064686, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012010
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 78732, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.4.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', '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': '78732.jm', 'subgroup_hash': 7886101597771740613, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012021
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': None, 'subgroup_hash': 5992888308001840125, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 187012032
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': 1699252334526339790, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.C_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 187012043
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': '78732.hj', 'subgroup_hash': 8978345343829813786, 'subgroup_order': 78732, 'subgroup_tex': 'C_3\\times C_3^6.S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 187012054
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': 3435913353402830545, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 187012065
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 52488, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': '52488.jq', 'subgroup_hash': 2281328934709253275, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012076
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 52488, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', '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': '52488.oy', 'subgroup_hash': 8700220178096497800, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012087
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 52488, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', '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': '52488.ox', 'subgroup_hash': 3759311292641453163, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012098
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 52488, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', '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': '52488.ow', 'subgroup_hash': 3513759125522374538, 'subgroup_order': 52488, 'subgroup_tex': 'C_9^2.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012109
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 52488, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.jo', 'subgroup_hash': 4665327327413083138, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.C_3:D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012121
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': None, 'subgroup_hash': 832420456558024707, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.C_6^2.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 187012132
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': '52488.iy', 'subgroup_hash': 3664175437981166824, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.(C_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 187012143
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8748, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': 1443315276032796636, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012154
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8496220518363085822, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.C_6^2.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 187012165
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7743094561058723542, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.C_6^2.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 187012176
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8748, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7952123966008757401, 'subgroup_order': 52488, 'subgroup_tex': 'C_3.C_3^5.C_6^2.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 187012187
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8748, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5966822828425210439, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.C_3^3.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012198
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3698427654733085255, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.C_3^3.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012209
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 801411566900584906, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^3.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012220
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8748, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3703496853480914171, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.C_3^3.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012232
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.P', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 625508867070580796, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^3.C_3^5.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012243
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.ix', 'subgroup_hash': 2745005805233058400, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.(C_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 187012254
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.oy', 'subgroup_hash': 8700220178096497800, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012265
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.ov', 'subgroup_hash': 1123493419083320473, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012276
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.ow', 'subgroup_hash': 3513759125522374538, 'subgroup_order': 52488, 'subgroup_tex': 'C_9^2.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012287
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.mq', 'subgroup_hash': 3577703088419704644, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012298
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.gp', 'subgroup_hash': 7970579071264152994, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012309
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.ig', 'subgroup_hash': 6996566918984081285, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5:C_6.S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 187012320
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.go', 'subgroup_hash': 3518561356633926969, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012331
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.mw', 'subgroup_hash': 235458569797744505, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012343
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.mx', 'subgroup_hash': 770095434173069907, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012354
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.mv', 'subgroup_hash': 351179261252739813, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 187012365
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.hn', 'subgroup_hash': 8299021092331319185, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 187012376
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.nm', 'subgroup_hash': 307095925315495375, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.C_3:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 187012387
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.nn', 'subgroup_hash': 5069278921576765591, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.C_3:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 187012398
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.np', 'subgroup_hash': 5399389086013256092, 'subgroup_order': 52488, 'subgroup_tex': 'C_9^2.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012409
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.gu', 'subgroup_hash': 5211067365169413248, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 187012420
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.gt', 'subgroup_hash': 5903859028673794019, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.(S_3\\times C_{12})', 'supersolvable': False, 'sylow': 0}
    • id: 187012431
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.nu', 'subgroup_hash': 588577563689325119, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5:C_6.S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 187012442
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BI', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.nw', 'subgroup_hash': 515990719860708515, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5:C_6.S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 187012454
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.nv', 'subgroup_hash': 2391715158201975375, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5:C_6.S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 187012465
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BK', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.if', 'subgroup_hash': 4436390459521974287, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012476
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BL', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.nm', 'subgroup_hash': 307095925315495375, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.C_3:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 187012487
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BM', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '52488.no', 'subgroup_hash': 1246405114934852587, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.C_3:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 187012498
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BN', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bn1', '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': '52488.np', 'subgroup_hash': 5399389086013256092, 'subgroup_order': 52488, 'subgroup_tex': 'C_9^2.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012509
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.6.BO', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bo1', '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': '52488.ho', 'subgroup_hash': 6323897529875163535, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^7.D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 187012520
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 39366, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', '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': 1942461814319229465, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^7.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 187012531
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 39366, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': 7326013364590921958, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 187012542
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 39366, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': 5012327402826289392, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^7.C_3.S_3', 'supersolvable': True, 'sylow': 0}
    • id: 187012553
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.8.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': 8521105485976409625, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^7.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 187012565
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.8.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': 4307832495625584967, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 187012576
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': 1959819664867548157, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 187012587
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': 3374030432317686061, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 187012598
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.A', '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': '34992.dx', 'subgroup_hash': 4930244027091316961, 'subgroup_order': 34992, 'subgroup_tex': '(C_3^3\\times C_6^2).S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 187012609
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.jj', 'subgroup_hash': 9007322163033318501, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 187012620
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8748, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6248299906695850824, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6.C_6.C_2^3', 'supersolvable': False, 'sylow': 0}
    • id: 187012631
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8748, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.js', 'subgroup_hash': 8433056192583596835, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6:(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 187012642
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8748, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.jt', 'subgroup_hash': 3454167135024616303, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 187012653
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 8748, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.jt', 'subgroup_hash': 3454167135024616303, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 187012664
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2916, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.mh', 'subgroup_hash': 2363467653671653785, 'subgroup_order': 34992, 'subgroup_tex': 'C_9^2.(C_6\\times S_3\\wr C_2)', 'supersolvable': False, 'sylow': 0}
    • id: 187012676
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 17496, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.jt', 'subgroup_hash': 3454167135024616303, 'subgroup_order': 34992, 'subgroup_tex': 'C_3^6.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
    • id: 187012687
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '34992.ji', 'subgroup_hash': 2381532525059986703, 'subgroup_order': 34992, 'subgroup_tex': '(C_3^3\\times S_3^2):D_{18}', 'supersolvable': False, 'sylow': 0}
    • id: 187012698
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '34992.mf', 'subgroup_hash': 1129249779306424604, 'subgroup_order': 34992, 'subgroup_tex': '(C_3^3\\times S_3^2).S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 187012709
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '34992.mg', 'subgroup_hash': 586094374532229909, 'subgroup_order': 34992, 'subgroup_tex': '(C_3^3\\times S_3^2).S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 187012720
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 5832, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.9.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '34992.me', 'subgroup_hash': 8601796198645737172, 'subgroup_order': 34992, 'subgroup_tex': '(C_3^3\\times S_3^2).S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 187012731
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', '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': 5301369469538973591, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 187012742
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': 4978039429070543318, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 187012753
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', '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': 491961529832568654, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 187012764
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1', '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': 5212786489665294296, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 187012775
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1', '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': 5580384718076822594, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 187012787
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1', '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': '26244.hp', 'subgroup_hash': 9052585708828590172, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^7.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 187012798
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1', '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': '26244.kg', 'subgroup_hash': 1925895142346900131, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 187012805
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.h1', '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': '26244.kf', 'subgroup_hash': 5064332461971179826, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 187012806
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.i1', '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': '26244.ke', 'subgroup_hash': 7942040550430954404, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 187012807
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.j1', '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': '26244.hq', 'subgroup_hash': 7650565741303806567, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^7.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 187012808
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.k1', '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': '26244.if', 'subgroup_hash': 722149402346531675, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^7.C_3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012809
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.l1', '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': '26244.ih', 'subgroup_hash': 4378958300222138567, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^4.C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012810
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.m1', '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': '26244.ku', 'subgroup_hash': 365237004022325326, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^4.C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012811
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.n1', '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': '26244.ks', 'subgroup_hash': 5598509489719865455, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^4.C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 187012812
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 26244, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.12.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.o1', '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': '26244.kv', 'subgroup_hash': 1722938225654411091, 'subgroup_order': 26244, 'subgroup_tex': 'C_9^2.C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 187011900
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '314928.nv', 'ambient_counter': 360, 'ambient_order': 314928, 'ambient_tex': 'C_3^7.D_6:D_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 4374, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '314928.nv.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': None, 'subgroup_hash': 8114048927791386552, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^5.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 915 matching records in this table.
    • id: 187011898
      {'ambient': '314928.nv', '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': [17, 607, 4, 39], 'generators': [2453133561843030035820, 365673361559968096105146, 15794720755311956739135, 13587033667, 6795281690365111297200, 551366640350668800, 158494346778656384294400, 20, 373, 13587033620, 29492292052877843755615, 64401664134855600, 316], 'label': '314928.nv.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': '314928.nv', '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': '314928.nv'}
    • id: 187011899
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '3.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': '6.A', 'coset_action_label': None, 'count': 3, 'diagramx': [23, -1, 103, -1], 'generators': [2453133561843030035820, 493367357150881920, 13587033667, 366, 6795281690365111297200, 20, 181076408405934180612494, 13587033620, 64401664134855600, 367923815629438861094574, 316, 161856655413382095667200], 'label': '314928.nv.3.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.B', 'old_label': '3.b1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.B', 'subgroup_fusion': None, 'weyl_group': '104976.id'}
    • id: 187011900
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.P', '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': '72.F', 'coset_action_label': None, 'count': 6, 'diagramx': [1572, -1, 1736, -1], 'generators': [2453389651822097242800, 1281227989574131200, 6795281690365111297200, 64401664134855600, 15794720755311956739120, 181, 316, 365673361559968096105141, 13587033600, 161856655413382095667200], 'label': '314928.nv.12.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.p1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.P', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011901
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.F', 'coset_action_label': None, 'count': 6, 'diagramx': [1406, -1, 1660, -1], 'generators': [181, 2453133561843030035815, 64401664134855600, 316, 13587033600, 6795281690365111297200, 1281227989574131200, 365673361559968096105141, 15794720755311956739120, 161856655413382095667200], 'label': '314928.nv.12.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.q1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Q', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011902
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1518, -1, 1711, -1], 'generators': [13587033620, 1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 15794720755311956739135, 316, 373, 2453389651822097242815, 161856655413382095667200], 'label': '314928.nv.12.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '12.r1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.R', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011903
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [903, -1, 1428, -1], 'generators': [424341963018654063309738, 64401664134855600, 2453389651822097242815, 316, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 373, 161856655413382095667200], 'label': '314928.nv.12.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.I', 'old_label': '12.s1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.S', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011904
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.T', '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': [1970, -1, 1920, -1], 'generators': [13587033620, 1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 316, 367923815629438861094574, 373, 2453389651822097242815, 161856655413382095667200], 'label': '314928.nv.12.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '12.t1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.T', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011905
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '144.B', 'coset_action_label': None, 'count': 12, 'diagramx': [123, -1, 1068, -1], 'generators': [1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 365673361559985299883061, 316, 367923815629438861094574, 373, 2453389651822097242815, 161856655413382095667200], 'label': '314928.nv.12.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '12.u1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.U', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011906
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '144.D', 'coset_action_label': None, 'count': 12, 'diagramx': [2394, -1, 2115, -1], 'generators': [1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 365673361559985299883061, 15794720755311956739135, 316, 373, 2453389651822097242815, 161856655413382095667200], 'label': '314928.nv.12.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.v1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.V', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011907
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.W', '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.C', 'coset_action_label': None, 'count': 6, 'diagramx': [2421, -1, 2128, -1], 'generators': [424341963018654063309738, 64401664134855600, 2453389651822097242815, 316, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 373, 161856655413382095667200], 'label': '314928.nv.12.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.M', 'old_label': '12.w1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.W', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011908
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.X', '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.D', 'coset_action_label': None, 'count': 6, 'diagramx': [1347, -1, 1633, -1], 'generators': [1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 15794720755311956739135, 316, 373, 2453389651822097242815, 422064779123451937944606, 161856655413382095667200], 'label': '314928.nv.12.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.N', 'old_label': '12.x1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.X', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011909
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '144.E', 'coset_action_label': None, 'count': 12, 'diagramx': [1543, -1, 1723, -1], 'generators': [424341963018654063309738, 64401664134855600, 2453389651822097242815, 422064779123451937944606, 316, 6795281690365111297200, 1281227989574131200, 20, 373, 161856655413382095667200], 'label': '314928.nv.12.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '12.y1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Y', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011910
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '3.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': '6.B', 'coset_action_label': None, 'count': 3, 'diagramx': [91, -1, 135, -1], 'generators': [2453133561843030035820, 29492317684322914987627, 493367357150881920, 55, 366, 6795281690365111297200, 424341963018654063309738, 20, 365673361559985299883061, 64401664134855600, 316, 161856655413382095667200], 'label': '314928.nv.3.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.C', 'old_label': '3.c1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.C', 'subgroup_fusion': None, 'weyl_group': '104976.nv'}
    • id: 187011911
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.Z', '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.E', 'coset_action_label': None, 'count': 6, 'diagramx': [1437, -1, 1674, -1], 'generators': [1281227989574131200, 20, 11325428965223940193215, 6795281690365111297200, 64401664134855600, 316, 373, 2453389651822097242815, 365673361559968096105146, 161856655413382095667200], 'label': '314928.nv.12.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.P', 'old_label': '12.z1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.Z', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011912
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BA', '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': '72.F', 'coset_action_label': None, 'count': 2, 'diagramx': [176, -1, 1092, -1], 'generators': [2453389651822097242800, 1281227989574131200, 6795281690365111297200, 64401664134855600, 15794720755311956739120, 316, 13587033600, 373, 365673361559968096105146, 161856655413382095667200], 'label': '314928.nv.12.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '12.ba1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BA', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011913
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '1296.C', 'coset_action_label': None, 'count': 24, 'diagramx': [422, -1, 1206, -1], 'generators': [1281227989574131200, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 15794720755311956739120, 316, 365673361559968096105141, 13587033600, 373, 161856655413382095667200], 'label': '314928.nv.12.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BB', 'old_label': '12.bb1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BB', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011914
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BC', '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': '144.F', 'coset_action_label': None, 'count': 6, 'diagramx': [270, -1, 1136, -1], 'generators': [1281227989574131200, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 15794720755311956739120, 316, 13587033600, 373, 365673361559968096105146, 161856655413382095667200], 'label': '314928.nv.12.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.bc1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011915
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BD', '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': '432.D', 'coset_action_label': None, 'count': 12, 'diagramx': [337, -1, 1166, -1], 'generators': [1281227989574131200, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 316, 365673361559968096105141, 13587033600, 15794720755311956739140, 373, 161856655413382095667200], 'label': '314928.nv.12.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BD', 'old_label': '12.bd1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011916
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BE', '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': '432.E', 'coset_action_label': None, 'count': 12, 'diagramx': [358, -1, 1176, -1], 'generators': [64401664134855600, 15794720755311956739135, 316, 13587033600, 6795281690365111297200, 1281227989574131200, 365673361559968096105141, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BE', 'old_label': '12.be1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011917
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '1296.D', 'coset_action_label': None, 'count': 24, 'diagramx': [401, -1, 1196, -1], 'generators': [64401664134855600, 15794720755311956739135, 316, 6795281690365111297200, 1281227989574131200, 365673361559968096105141, 13587033615, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BF', 'old_label': '12.bf1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011918
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '1296.F', 'coset_action_label': None, 'count': 24, 'diagramx': [379, -1, 1186, -1], 'generators': [64401664134855600, 15794720755311956739135, 316, 6795281690365111297200, 1281227989574131200, 365673361559968096105141, 13587033620, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BG', 'old_label': '12.bg1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BG', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011919
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BH', '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': '432.F', 'coset_action_label': None, 'count': 12, 'diagramx': [315, -1, 1157, -1], 'generators': [13587033615, 1281227989574131200, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 316, 365673361559968096105141, 15794720755311956739140, 373, 161856655413382095667200], 'label': '314928.nv.12.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BH', 'old_label': '12.bh1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BH', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011920
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BI', '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': '432.G', 'coset_action_label': None, 'count': 12, 'diagramx': [443, -1, 1216, -1], 'generators': [13587033620, 1281227989574131200, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 15794720755311956739120, 316, 365673361559968096105141, 373, 161856655413382095667200], 'label': '314928.nv.12.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BI', 'old_label': '12.bi1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BI', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011921
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '3.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': '6.C', 'coset_action_label': None, 'count': 3, 'diagramx': [57, -1, 119, -1], 'generators': [2453133561843030035820, 29492279247943541842020, 15794720755311956739135, 493367357150881920, 55, 366, 6795281690365111297200, 20, 64401664134855600, 316, 161856655413382095667200, 422064779123451937944606], 'label': '314928.nv.3.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.D', 'old_label': '3.d1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.D', 'subgroup_fusion': None, 'weyl_group': '104976.nw'}
    • id: 187011922
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '1296.G', 'coset_action_label': None, 'count': 24, 'diagramx': [293, -1, 1147, -1], 'generators': [13587033620, 1281227989574131200, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 15794720755311956739120, 316, 373, 365673361559968096105146, 161856655413382095667200], 'label': '314928.nv.12.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BJ', 'old_label': '12.bj1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BJ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011923
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BK', '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': '432.H', 'coset_action_label': None, 'count': 12, 'diagramx': [466, -1, 1226, -1], 'generators': [13587033615, 1281227989574131200, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 15794720755311956739135, 316, 373, 365673361559968096105146, 161856655413382095667200], 'label': '314928.nv.12.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.BK', 'old_label': '12.bk1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BK', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011924
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '144.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2254, -1, 2050, -1], 'generators': [64401664134855600, 15794720755311956739135, 316, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '12.bl1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BL', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011925
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1065, -1, 1502, -1], 'generators': [424341963018654063309738, 64401664134855600, 316, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.I', 'old_label': '12.bm1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BM', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011926
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BN', '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': [1168, -1, 1550, -1], 'generators': [13587033620, 1281227989574131200, 20, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 316, 367923815629438861094574, 373, 161856655413382095667200], 'label': '314928.nv.12.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.J', 'old_label': '12.bn1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BN', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011927
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.B', 'coset_action_label': None, 'count': 12, 'diagramx': [1758, -1, 1822, -1], 'generators': [1281227989574131200, 20, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 365673361559985299883061, 316, 367923815629438861094574, 373, 161856655413382095667200], 'label': '314928.nv.12.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '12.bo1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BO', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011928
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BP', '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.D', 'coset_action_label': None, 'count': 12, 'diagramx': [1889, -1, 1883, -1], 'generators': [64401664134855600, 15794720755311956739135, 316, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.bp1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BP', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011929
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '48.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1216, -1, 1572, -1], 'generators': [424341963018654063309738, 64401664134855600, 316, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.M', 'old_label': '12.bq1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BQ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011930
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.D', 'coset_action_label': None, 'count': 6, 'diagramx': [1862, -1, 1870, -1], 'generators': [64401664134855600, 422064779123451937944606, 15794720755311956739135, 316, 6795281690365111297200, 1281227989574131200, 20, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.N', 'old_label': '12.br1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BR', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011931
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '144.E', 'coset_action_label': None, 'count': 12, 'diagramx': [1374, -1, 1645, -1], 'generators': [424341963018654063309738, 64401664134855600, 422064779123451937944606, 316, 6795281690365111297200, 1281227989574131200, 20, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '12.bs1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BS', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011932
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '3.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.D', 'coset_action_label': None, 'count': 3, 'diagramx': [125, -1, 150, -1], 'generators': [2453133561843030035820, 365673361559968096105146, 493367357150881920, 55, 366, 6795281690365111297200, 20, 11325428965223940193215, 29492292052877843755615, 64401664134855600, 316, 161856655413382095667200], 'label': '314928.nv.3.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '3.e1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.E', 'subgroup_fusion': None, 'weyl_group': '104976.nu'}
    • id: 187011933
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '48.E', 'coset_action_label': None, 'count': 6, 'diagramx': [2119, -1, 1989, -1], 'generators': [1281227989574131200, 20, 2453133561843030035820, 11325428965223940193215, 6795281690365111297200, 64401664134855600, 316, 373, 365673361559968096105146, 161856655413382095667200], 'label': '314928.nv.12.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.P', 'old_label': '12.bt1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BT', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011934
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BU', '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': '144.F', 'coset_action_label': None, 'count': 6, 'diagramx': [1143, -1, 1538, -1], 'generators': [1281227989574131200, 6795281690365111297200, 13587033655, 64401664134855600, 15794720755311956739120, 181, 316, 365673361559968096105141, 13587033600, 161856655413382095667200], 'label': '314928.nv.12.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.bu1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BU', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011935
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.A', 'coset_action_label': None, 'count': 2, 'diagramx': [2298, -1, 2071, -1], 'generators': [13587033620, 1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 15794720755311956739135, 13587033667, 316, 373, 161856655413382095667200], 'label': '314928.nv.12.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '12.bv1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BV', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011936
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.B', 'coset_action_label': None, 'count': 2, 'diagramx': [728, -1, 1347, -1], 'generators': [1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 365673361559985299883061, 316, 367923815629438861094574, 373, 55, 161856655413382095667200], 'label': '314928.nv.12.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '12.bw1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BW', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011937
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '36.D', 'coset_action_label': None, 'count': 2, 'diagramx': [881, -1, 1418, -1], 'generators': [64401664134855600, 15794720755311956739135, 316, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 55, 373, 161856655413382095667200], 'label': '314928.nv.12.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '12.bx1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BX', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011938
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '36.E', 'coset_action_label': None, 'count': 2, 'diagramx': [806, -1, 1383, -1], 'generators': [424341963018654063309738, 64401664134855600, 422064779123451937944606, 316, 6795281690365111297200, 1281227989574131200, 20, 55, 373, 161856655413382095667200], 'label': '314928.nv.12.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '12.by1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BY', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011939
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '144.F', 'coset_action_label': None, 'count': 6, 'diagramx': [1915, -1, 1895, -1], 'generators': [64401664134855600, 15794720755311956739135, 13587033734, 6795281690365111297200, 1281227989574131200, 20, 365673361559968096104960, 13587033620, 33828658551564679232780, 161856655413382095667200], 'label': '314928.nv.12.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.U', 'old_label': '12.bz1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.BZ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011940
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CA', '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': '72.F', 'coset_action_label': None, 'count': 6, 'diagramx': [246, -1, 1125, -1], 'generators': [13587033660, 181, 64401664134855600, 13587033600, 6795281690365111297200, 1281227989574131200, 365673361559968096105141, 15794720755311956739120, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.ca1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CA', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011941
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CB', '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': '72.F', 'coset_action_label': None, 'count': 6, 'diagramx': [223, -1, 1114, -1], 'generators': [64401664134855600, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 365673361559968096104960, 13587033620, 13587033667, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.U', 'old_label': '12.cb1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CB', 'subgroup_fusion': None, 'weyl_group': '52488.mq'}
    • id: 187011942
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CC', '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': '144.F', 'coset_action_label': None, 'count': 6, 'diagramx': [1264, -1, 1594, -1], 'generators': [29492292052877843755454, 64401664134855600, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 365673361559968096104960, 13587033620, 13587033667, 161856655413382095667200], 'label': '314928.nv.12.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.U', 'old_label': '12.cc1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011943
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '4.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.A', 'coset_action_label': None, 'count': 1, 'diagramx': [166, 2855, 244, 1231], 'generators': [13587033620, 20, 6795281690365111297200, 64401664134855600, 366, 15794720755311956739135, 13587033667, 316, 365673361559968096105146, 161856655413382095667200, 493367357150881920], 'label': '314928.nv.4.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.A', 'subgroup_fusion': None, 'weyl_group': '34992.jo'}
    • id: 187011944
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CD', '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': '144.F', 'coset_action_label': None, 'count': 6, 'diagramx': [200, -1, 1104, -1], 'generators': [1281227989574131200, 6795281690365111297200, 2453133561843030036101, 64401664134855600, 15794720755311956739120, 181, 365673361559968096105141, 13587033667, 13587033600, 161856655413382095667200], 'label': '314928.nv.12.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '12.cd1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011945
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1240, -1, 1583, -1], 'generators': [13587033620, 1281227989574131200, 20, 6795281690365111297200, 424341963018654063309738, 64401664134855600, 13587033667, 373, 33828658551564679232780, 161856655413382095667200], 'label': '314928.nv.12.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.A', 'old_label': '12.ce1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011946
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CF', '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': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2225, -1, 2037, -1], 'generators': [64401664134855600, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 373, 13587033667, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '12.cf1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011947
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 3, 'diagramx': [1654, -1, 1774, -1], 'generators': [424341963018654063309738, 64401664134855600, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 373, 13587033667, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.A', 'old_label': '12.cg1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CG', 'subgroup_fusion': None, 'weyl_group': '104976.ie'}
    • id: 187011948
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CH', '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': 3, 'diagramx': [1942, -1, 1907, -1], 'generators': [13587033620, 1281227989574131200, 20, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 13587033667, 367923815629438861094574, 373, 161856655413382095667200], 'label': '314928.nv.12.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.B', 'old_label': '12.ch1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CH', 'subgroup_fusion': None, 'weyl_group': '104976.id'}
    • id: 187011949
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '72.B', 'coset_action_label': None, 'count': 6, 'diagramx': [753, -1, 1358, -1], 'generators': [64401664134855600, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 55, 367923815629438861094574, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '12.ci1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CI', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011950
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '72.D', 'coset_action_label': None, 'count': 6, 'diagramx': [1292, -1, 1607, -1], 'generators': [64401664134855600, 15794720755311956739135, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 55, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.cj1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CJ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011951
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CK', '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.C', 'coset_action_label': None, 'count': 3, 'diagramx': [1464, -1, 1687, -1], 'generators': [424341963018654063309738, 64401664134855600, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 55, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.C', 'old_label': '12.ck1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CK', 'subgroup_fusion': None, 'weyl_group': '104976.nv'}
    • id: 187011952
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '24.D', 'coset_action_label': None, 'count': 3, 'diagramx': [1626, -1, 1761, -1], 'generators': [64401664134855600, 422064779123451937944606, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 55, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.D', 'old_label': '12.cl1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CL', 'subgroup_fusion': None, 'weyl_group': '104976.nw'}
    • id: 187011953
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CM', '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': '72.E', 'coset_action_label': None, 'count': 6, 'diagramx': [492, -1, 1238, -1], 'generators': [424341963018654063309738, 64401664134855600, 422064779123451937944606, 6795281690365111297200, 1281227989574131200, 20, 55, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '12.cm1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CM', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011954
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '4.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': '4.B', 'coset_action_label': None, 'count': 1, 'diagramx': [99, 2204, 212, 1139], 'generators': [13587033620, 20, 6795281690365111297200, 64401664134855600, 366, 15794720755311956739135, 13587033667, 365673361559968096105146, 33828658551564679232780, 493367357150881920, 161856655413382095667200], 'label': '314928.nv.4.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.B', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011955
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CN', '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': 3, 'diagramx': [1320, -1, 1620, -1], 'generators': [64401664134855600, 11325428965223940193215, 6795281690365111297200, 1281227989574131200, 20, 55, 373, 365673361559968096105146, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.CN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '12.cn1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CN', 'subgroup_fusion': None, 'weyl_group': '104976.nu'}
    • id: 187011956
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CO', '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': 3, 'diagramx': [1193, -1, 1561, -1], 'generators': [13587033620, 1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 13587033667, 367923815629438861094574, 373, 29492292052877843755615, 161856655413382095667200], 'label': '314928.nv.12.CO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.B', 'old_label': '12.co1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CO', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011957
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CP', '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.C', 'coset_action_label': None, 'count': 3, 'diagramx': [1836, -1, 1858, -1], 'generators': [424341963018654063309738, 64401664134855600, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 29492292052877843755615, 55, 373, 161856655413382095667200], 'label': '314928.nv.12.CP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.C', 'old_label': '12.cp1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CP', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011958
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CQ', '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': 3, 'diagramx': [59, -1, 1039, -1], 'generators': [64401664134855600, 422064779123451937944606, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 29492292052877843755615, 55, 373, 161856655413382095667200], 'label': '314928.nv.12.CQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.D', 'old_label': '12.cq1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CQ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011959
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CR', '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': 3, 'diagramx': [1704, -1, 1797, -1], 'generators': [1281227989574131200, 20, 11325428965223940193215, 6795281690365111297200, 64401664134855600, 373, 365673361559968096105146, 29492292052877843755615, 161856655413382095667200, 55], 'label': '314928.nv.12.CR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '12.cr1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CR', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011960
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CS', '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': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1119, -1, 1527, -1], 'generators': [64401664134855600, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 373, 13587033667, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.12.CS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '12.cs1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CS', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011961
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CT', '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.A', 'coset_action_label': None, 'count': 3, 'diagramx': [782, -1, 1372, -1], 'generators': [424341963018654063309738, 64401664134855600, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 373, 13587033667, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.12.CT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.A', 'old_label': '12.ct1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CT', 'subgroup_fusion': None, 'weyl_group': '104976.ie'}
    • id: 187011962
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CU', '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': 3, 'diagramx': [2515, -1, 2171, -1], 'generators': [13587033620, 1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 13587033667, 367923815629438861094574, 373, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.12.CU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.B', 'old_label': '12.cu1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CU', 'subgroup_fusion': None, 'weyl_group': '104976.id'}
    • id: 187011963
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CV', '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': '72.B', 'coset_action_label': None, 'count': 6, 'diagramx': [520, -1, 1251, -1], 'generators': [64401664134855600, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 55, 367923815629438861094574, 373, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.12.CV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.K', 'old_label': '12.cv1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CV', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011964
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CW', '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': '72.D', 'coset_action_label': None, 'count': 6, 'diagramx': [1786, -1, 1835, -1], 'generators': [64401664134855600, 15794720755311956739135, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 55, 373, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.12.CW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.L', 'old_label': '12.cw1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CW', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011965
      {'ambient': '314928.nv', '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': [18, 623, 175, 915], 'generators': [13587033620, 20, 2453133561843030035820, 6795281690365111297200, 64401664134855600, 366, 15794720755311956739135, 13587033667, 365673361559968096105146, 493367357150881920, 161856655413382095667200], 'label': '314928.nv.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': '314928.nv', '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': '314928.nv'}
    • id: 187011966
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CX', '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.C', 'coset_action_label': None, 'count': 3, 'diagramx': [2171, -1, 2013, -1], 'generators': [424341963018654063309738, 64401664134855600, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 55, 373, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.12.CX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.C', 'old_label': '12.cx1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CX', 'subgroup_fusion': None, 'weyl_group': '104976.nv'}
    • id: 187011967
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CY', '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': 3, 'diagramx': [830, -1, 1394, -1], 'generators': [64401664134855600, 422064779123451937944606, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 55, 373, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.12.CY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.D', 'old_label': '12.cy1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CY', 'subgroup_fusion': None, 'weyl_group': '104976.nw'}
    • id: 187011968
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.CZ', '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': '72.E', 'coset_action_label': None, 'count': 6, 'diagramx': [857, -1, 1407, -1], 'generators': [424341963018654063309738, 64401664134855600, 422064779123451937944606, 6795281690365111297200, 1281227989574131200, 20, 55, 373, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.12.CZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.O', 'old_label': '12.cz1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.CZ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011969
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DA', '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': 3, 'diagramx': [2092, -1, 1976, -1], 'generators': [64401664134855600, 11325428965223940193215, 6795281690365111297200, 1281227989574131200, 20, 55, 373, 365673361559968096105146, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.12.DA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '12.da1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DA', 'subgroup_fusion': None, 'weyl_group': '104976.nu'}
    • id: 187011970
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DB', '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.A', 'coset_action_label': None, 'count': 3, 'diagramx': [2490, -1, 2159, -1], 'generators': [13587033620, 1281227989574131200, 20, 6795281690365111297200, 424341963018654063309738, 64401664134855600, 33828658551564679233298, 13587033667, 373, 161856655413382095667200], 'label': '314928.nv.12.DB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.F', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.A', 'old_label': '12.db1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DB', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011971
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '24.B', 'coset_action_label': None, 'count': 3, 'diagramx': [2370, -1, 2104, -1], 'generators': [13587033620, 1281227989574131200, 20, 6795281690365111297200, 64401664134855600, 29492292052877843755787, 13587033667, 367923815629438861094574, 373, 161856655413382095667200], 'label': '314928.nv.12.DC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.B', 'old_label': '12.dc1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011972
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '24.C', 'coset_action_label': None, 'count': 3, 'diagramx': [571, -1, 1275, -1], 'generators': [424341963018654063309738, 64401664134855600, 29492292052877843755787, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 55, 373, 161856655413382095667200], 'label': '314928.nv.12.DD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.C', 'old_label': '12.dd1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011973
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DE', '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': 3, 'diagramx': [1092, -1, 1515, -1], 'generators': [64401664134855600, 422064779123451937944606, 15794720755311956739135, 29492292052877843755787, 6795281690365111297200, 1281227989574131200, 20, 55, 373, 161856655413382095667200], 'label': '314928.nv.12.DE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.D', 'old_label': '12.de1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011974
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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': '24.E', 'coset_action_label': None, 'count': 3, 'diagramx': [952, -1, 1450, -1], 'generators': [1281227989574131200, 20, 11325428965223940193215, 6795281690365111297200, 64401664134855600, 29492292052877843755787, 373, 365673361559968096105146, 55, 161856655413382095667200], 'label': '314928.nv.12.DF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.G', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.E', 'old_label': '12.df1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011975
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.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.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1492, -1, 1699, -1], 'generators': [181076408405934180612494, 424341963018654063309738, 64401664134855600, 2453389651822097242815, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 373, 161856655413382095667200], 'label': '314928.nv.12.DG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.V', 'old_label': '12.dg1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DG', 'subgroup_fusion': None, 'weyl_group': '17496.it'}
    • id: 187011976
      {'ambient': '314928.nv', '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': 1, 'contained_in': None, 'contains': None, 'core': '4.D', 'coset_action_label': None, 'count': 1, 'diagramx': [72, 1414, 200, 1027], 'generators': [366, 64401664134855600, 15794720755311956739135, 6795281690365111297200, 20, 29492292052877843755615, 13587033620, 13587033667, 365673361559968096105146, 161856655413382095667200, 493367357150881920], 'label': '314928.nv.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': '314928.nv', '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': None}
    • id: 187011977
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DH', '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': '72.F', 'coset_action_label': None, 'count': 6, 'diagramx': [1037, -1, 1489, -1], 'generators': [2453389651822097242800, 1281227989574131200, 6795281690365111297200, 64401664134855600, 15794720755311956739120, 366, 13587033600, 365673361559968096105134, 29492292052877843755615, 161856655413382095667200], 'label': '314928.nv.12.DH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.U', 'old_label': '12.dh1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DH', 'subgroup_fusion': None, 'weyl_group': '17496.fs'}
    • id: 187011978
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DI', '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.A', 'coset_action_label': None, 'count': 6, 'diagramx': [38, -1, 1029, -1], 'generators': [181076408405934180612494, 424341963018654063309738, 64401664134855600, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.DI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.V', 'old_label': '12.di1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DI', 'subgroup_fusion': None, 'weyl_group': '52488.gp'}
    • id: 187011979
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DJ', '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': '144.F', 'coset_action_label': None, 'count': 6, 'diagramx': [994, -1, 1470, -1], 'generators': [29492292052877843755454, 64401664134855600, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 365673361559968096104960, 13587033620, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.DJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.U', 'old_label': '12.dj1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DJ', 'subgroup_fusion': None, 'weyl_group': '52488.mq'}
    • id: 187011980
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DK', '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': '432.D', 'coset_action_label': None, 'count': 12, 'diagramx': [1014, -1, 1479, -1], 'generators': [64401664134855600, 29492292052877843755819, 6795281690365111297200, 1281227989574131200, 20, 365673361559968096105333, 13587033620, 15794720755311956739498, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.DK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.DK', 'old_label': '12.dk1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DK', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011981
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DL', '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': [2447, -1, 2140, -1], 'generators': [181076408405934180612494, 64401664134855600, 2453389651822097242815, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 367923815629438861094574, 373, 161856655413382095667200], 'label': '314928.nv.12.DL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.X', 'old_label': '12.dl1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DL', 'subgroup_fusion': None, 'weyl_group': '17496.hz'}
    • id: 187011982
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DM', '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.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1730, -1, 1809, -1], 'generators': [424341963018654063309738, 64401664134855600, 2453389651822097242815, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 20, 373, 161856655413382095667200, 29492279247943541842020], 'label': '314928.nv.12.DM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.Y', 'old_label': '12.dm1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DM', 'subgroup_fusion': None, 'weyl_group': '17496.nn'}
    • id: 187011983
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DN', '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.D', 'coset_action_label': None, 'count': 6, 'diagramx': [2322, -1, 2082, -1], 'generators': [64401664134855600, 2453389651822097242815, 422064779123451937944606, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 29492292052877843755615, 373, 161856655413382095667200], 'label': '314928.nv.12.DN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.Z', 'old_label': '12.dn1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DN', 'subgroup_fusion': None, 'weyl_group': '5000.cw'}
    • id: 187011984
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DO', '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.E', 'coset_action_label': None, 'count': 6, 'diagramx': [150, -1, 1081, -1], 'generators': [1281227989574131200, 20, 11325428965223940193215, 6795281690365111297200, 29492317684322914987627, 64401664134855600, 373, 2453389651822097242815, 365673361559968096105146, 161856655413382095667200], 'label': '314928.nv.12.DO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.BA', 'old_label': '12.do1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DO', 'subgroup_fusion': None, 'weyl_group': '17496.nm'}
    • id: 187011985
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DP', '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': '72.F', 'coset_action_label': None, 'count': 2, 'diagramx': [2347, -1, 2094, -1], 'generators': [29492292052877843755454, 64401664134855600, 2453389651822097242815, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 365673361559968096104960, 13587033620, 161856655413382095667200], 'label': '314928.nv.12.DP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '12.dp1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DP', 'subgroup_fusion': None, 'weyl_group': '52488.mq'}
    • id: 187011986
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DQ', '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': [2064, -1, 1963, -1], 'generators': [181076408405934180612494, 64401664134855600, 6795281690365111297200, 1281227989574131200, 20, 13587033620, 367923815629438861094574, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.DQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.X', 'old_label': '12.dq1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DQ', 'subgroup_fusion': None, 'weyl_group': '52488.go'}
    • id: 187011987
      {'ambient': '314928.nv', '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': [214, 3461, 266, 1317], 'generators': [13587033620, 20, 6795281690365111297200, 64401664134855600, 366, 15794720755311956739135, 13587033667, 365673361559968096105146, 493367357150881920, 161856655413382095667200, 2453133561843030036293], 'label': '314928.nv.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': '314928.nv', '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': '314928.nv'}
    • id: 187011988
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DR', '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.C', 'coset_action_label': None, 'count': 6, 'diagramx': [1998, -1, 1933, -1], 'generators': [424341963018654063309738, 64401664134855600, 6795281690365111297200, 365673361559985299883061, 1281227989574131200, 29492317684322914987627, 20, 373, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.DR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.Y', 'old_label': '12.dr1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DR', 'subgroup_fusion': None, 'weyl_group': '52488.mw'}
    • id: 187011989
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DS', '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.D', 'coset_action_label': None, 'count': 6, 'diagramx': [705, -1, 1336, -1], 'generators': [64401664134855600, 422064779123451937944606, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 20, 373, 161856655413382095667200, 2453133561843030035820, 29492279247943541842020], 'label': '314928.nv.12.DS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.Z', 'old_label': '12.ds1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DS', 'subgroup_fusion': None, 'weyl_group': '52488.mx'}
    • id: 187011990
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DT', '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.E', 'coset_action_label': None, 'count': 6, 'diagramx': [1599, -1, 1748, -1], 'generators': [64401664134855600, 11325428965223940193215, 6795281690365111297200, 1281227989574131200, 20, 29492292052877843755615, 373, 365673361559968096105146, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.DT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.BA', 'old_label': '12.dt1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DT', 'subgroup_fusion': None, 'weyl_group': '52488.mv'}
    • id: 187011991
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DU', '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': '144.F', 'coset_action_label': None, 'count': 6, 'diagramx': [595, -1, 1286, -1], 'generators': [365673361559968096105134, 366, 64401664134855600, 13587033600, 6795281690365111297200, 1281227989574131200, 29492292052877843755620, 15794720755311956739120, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.DU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.U', 'old_label': '12.du1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DU', 'subgroup_fusion': None, 'weyl_group': '52488.mq'}
    • id: 187011992
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DV', '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': '432.E', 'coset_action_label': None, 'count': 12, 'diagramx': [681, -1, 1325, -1], 'generators': [366, 64401664134855600, 13587033600, 6795281690365111297200, 1281227989574131200, 365673361559968096105141, 29492292052877843755627, 161856655413382095667200, 2453133561843030035820, 15794720755311956739140], 'label': '314928.nv.12.DV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.DV', 'old_label': '12.dv1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DV', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011993
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DW', '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': '432.F', 'coset_action_label': None, 'count': 12, 'diagramx': [617, -1, 1296, -1], 'generators': [366, 64401664134855600, 15794720755311956739135, 6795281690365111297200, 1281227989574131200, 365673361559968096105141, 29492292052877843755627, 13587033620, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.DW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.DW', 'old_label': '12.dw1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DW', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011994
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DX', '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': '432.G', 'coset_action_label': None, 'count': 12, 'diagramx': [639, -1, 1306, -1], 'generators': [366, 64401664134855600, 6795281690365111297200, 1281227989574131200, 29492292052877843755615, 13587033620, 15794720755311956739120, 365673361559968096105146, 161856655413382095667200, 2453133561843030035820], 'label': '314928.nv.12.DX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.DX', 'old_label': '12.dx1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DX', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011995
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '12.DY', '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': '432.H', 'coset_action_label': None, 'count': 12, 'diagramx': [661, -1, 1316, -1], 'generators': [365673361559968096105134, 366, 64401664134855600, 6795281690365111297200, 1281227989574131200, 29492292052877843755620, 13587033620, 161856655413382095667200, 2453133561843030035820, 15794720755311956739140], 'label': '314928.nv.12.DY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.DY', 'old_label': '12.dy1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.DY', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 187011996
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '16.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': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [16, 558, 2193, 3763], 'generators': [64401664134855600, 15794720755311956739135, 2308971973569648634800, 1281227989574131200, 20, 13587033620, 373, 365673361559968096105146, 161856655413382095667200], 'label': '314928.nv.16.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '3888.gd'}
    • id: 187011997
      {'ambient': '314928.nv', 'aut_centralizer_order': None, 'aut_label': '18.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '18.A', 'coset_action_label': None, 'count': 1, 'diagramx': [2826, 646, 3498, 3858], 'generators': [20, 158494346778656384294400, 397038065847604547753655, 551366640350668800, 316, 25987943544116400, 2308971973569648634800, 2308971973569648634855, 373, 428884146376512972728058], 'label': '314928.nv.18.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '314928.nv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.A', 'subgroup_fusion': None, 'weyl_group': None}