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  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [36, 18, 6, 6, 12], 'aut_gens': [[223383498153158185171252046349548996212434, 170184613510976278886462041186110401542466, 169892903224118056970887953686373897994197], [297835893202748373700986601032766766629174, 371989532658158574079018698259682051882635, 234011624019122947177955570622411812366038], [351031271778427043695839040078287266759518, 170184868418974558453768557975702983679605, 307873808361558040815949628944122109441653], [42244874964980320832134511950740314954733, 371989532658158961859267469565955579025039, 351031526695571973601501838863551540205914], [52872729451047871920453908526400629038154, 244341504390473027568260261277832323556292, 96030973789985713038032409133495313750877], [32206959779950256055833520055289997613917, 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'aut_phi_ratio': 36.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [2, 243, 2, 2], [2, 729, 1, 2], [3, 2, 1, 2], [3, 2, 2, 1], [3, 3, 1, 2], [3, 4, 1, 2], [3, 4, 2, 2], [3, 6, 1, 5], [3, 6, 2, 5], [3, 6, 3, 3], [3, 8, 1, 2], [3, 8, 2, 2], [3, 12, 1, 8], [3, 12, 2, 23], [3, 12, 3, 3], [3, 12, 4, 3], [3, 12, 6, 6], [3, 12, 12, 3], [3, 24, 1, 11], [3, 24, 2, 51], [3, 24, 3, 6], [3, 24, 4, 30], [3, 24, 6, 33], [3, 24, 12, 24], [6, 162, 1, 2], [6, 243, 1, 2], [6, 243, 2, 2], [6, 324, 1, 1], [6, 486, 1, 5], [6, 486, 2, 11], [6, 486, 3, 3], [6, 486, 6, 3], [6, 729, 1, 4], [6, 729, 2, 2], [6, 972, 1, 3], [6, 972, 2, 10], [6, 972, 3, 3], [6, 972, 4, 3], [6, 972, 6, 6], [6, 972, 12, 3], [6, 1458, 1, 6], [6, 1458, 2, 11], [6, 2916, 1, 6], [6, 2916, 2, 15], [9, 486, 1, 3], [9, 972, 1, 3], [9, 972, 2, 3], [9, 1944, 1, 3], [9, 1944, 2, 6], [18, 4374, 1, 3], [18, 4374, 2, 3], [18, 8748, 1, 3], [18, 8748, 2, 3]], 'aut_supersolvable': False, 'aut_tex': 'C_3^8.C_6^3.C_2^2', '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': 1329108309948349558, 'autcentquo_nilpotent': False, 'autcentquo_order': 5668704, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^8.C_6.C_6^2.C_2^2', 'cc_stats': [[1, 1, 1], [2, 81, 1], [2, 243, 4], [2, 729, 2], [3, 2, 4], [3, 3, 2], [3, 4, 6], [3, 6, 24], [3, 8, 6], [3, 12, 147], [3, 24, 737], [6, 162, 2], [6, 243, 6], [6, 324, 1], [6, 486, 54], [6, 729, 8], [6, 972, 116], [6, 1458, 28], [6, 2916, 36], [9, 486, 3], [9, 972, 9], [9, 1944, 15], [18, 4374, 9], [18, 8748, 9]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '472392.dm', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': False, 'counter': 91, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 81, 1, 1], [2, 243, 1, 4], [2, 729, 1, 2], [3, 2, 1, 4], [3, 3, 2, 1], [3, 4, 1, 6], [3, 6, 1, 6], [3, 6, 2, 9], [3, 8, 1, 6], [3, 12, 1, 27], [3, 12, 2, 60], [3, 24, 1, 57], [3, 24, 2, 340], [6, 162, 1, 2], [6, 243, 2, 3], [6, 324, 1, 1], [6, 486, 1, 20], [6, 486, 2, 17], [6, 729, 2, 4], [6, 972, 1, 24], [6, 972, 2, 46], [6, 1458, 1, 8], [6, 1458, 2, 10], [6, 2916, 1, 8], [6, 2916, 2, 14], [9, 486, 1, 1], [9, 486, 2, 1], [9, 972, 1, 3], [9, 972, 2, 3], [9, 1944, 1, 5], [9, 1944, 2, 5], [18, 4374, 1, 3], [18, 4374, 2, 3], [18, 8748, 1, 3], [18, 8748, 2, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 18, 'exponents_of_order': [10, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 156], [24, 1, 6]], 'familial': False, 'frattini_label': '243.67', 'frattini_quotient': '1944.3935', 'hash': 2494925307747966133, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 18, 6], 'inner_gens': [[223383498153158185171252046349548996212434, 52583718513715615446891581183820953213375, 307873553453559761352051179444834072062674], [351031271787573694034185590465926251428238, 170184613510976278886462041186110401542466, 287207257520787890243682457970236752808054], [96030973780839062751382472248937204976718, 42545277084695207271014767855744007971915, 169892903224118056970887953686373897994197]], 'inner_hash': 2494925307747966133, 'inner_nilpotent': False, 'inner_order': 472392, 'inner_split': True, 'inner_tex': 'C_3^7.S_3^3', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 24], [2, 48], [4, 36], [6, 76], [8, 18], [12, 288], [24, 740]], 'label': '472392.dm', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^7.S3^3', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 364, 'number_characteristic_subgroups': 79, 'number_conjugacy_classes': 1230, 'number_divisions': 711, 'number_normal_subgroups': 217, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 472392, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 2511], [3, 19682], [6, 292734], [9, 39366], [18, 118098]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [10628907044783947027978816427442679872000, 0], 'outer_gens': [[287207783773314688541424240132364338042933, 233713394970185186110172716790715566461891, 371698093972872782166537525095915735917914], [116696743461083716759335686743086540186958, 52583463588033005385610590582120562385276, 180521283989543387238733365330437072154694]], 'outer_group': '12.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [24, 748], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 24], [4, 28], [6, 28], [8, 18], [12, 84], [16, 6], [24, 176], [48, 339]], 'representations': {'PC': {'code': '951028824443875016441838094677424939856245091172749496858879931837327050338568137685436461808413688481574736288901493025889524826334554117900903661753436020690828252019037355870505168973266841655138316618431966805021071179262616916268440241570340870983887743', 'gens': [1, 3, 6, 8, 9, 10, 11, 12, 13], 'pres': [13, -2, -3, -2, -3, -3, -2, -3, -3, 3, 3, 3, 3, 3, 26, 14154896, 9150000, 106, 16242723, 8509504, 198, 21275284, 160061, 5538798, 4235899, 2249954, 709311, 226, 9159702, 1962356, 979569, 24732871, 7660257, 4071646, 1320, 16376264, 3980374, 1623773, 113095, 6402249, 5489675, 533568, 14114, 26131258, 262584, 3729775, 109899, 56710379, 3319093, 2013386, 151708, 68554524, 11425790, 1560597, 492881]}, 'Perm': {'d': 36, 'gens': [223383498153158185171252046349548996212434, 170184613510976278886462041186110401542466, 169892903224118056970887953686373897994197]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 3, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^7.S_3^3', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • ['group_order', 'group_counter'] [472392, 91] does not appear in gps_conj_classes
  • group 472392.dm does not appear in gps_qchar
  • group 472392.dm does not appear in gps_char
  • gps_subgroup_search • Show schema
    Showing the first 100 of 152 matching records in this table.
    • id: 217018984
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 472392, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '472392.dm.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': '472392.dm', 'subgroup_hash': 2494925307747966133, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^7.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 217019048
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 236196, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.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': '236196.en', 'subgroup_hash': 178057120058620742, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^8.S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 217019059
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 236196, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.eh', 'subgroup_hash': 5068959990398574119, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^8.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 217019070
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 236196, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.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': None, 'subgroup_hash': 1683389583167315696, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^8.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 217019081
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.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': '236196.ep', 'subgroup_hash': 3243472356451137290, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^8.S_3^2', 'supersolvable': True, 'sylow': 0}
    • id: 217019092
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.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': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 980442718726258908, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^7.C_3.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 217019103
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 157464, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.3.A', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.fc', 'subgroup_hash': 2803238966435243816, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 217019114
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.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': '157464.eu', 'subgroup_hash': 8466846343459247350, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 217019125
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.3.C', 'maximal': True, 'maximal_normal': False, 'metabelian': True, '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': None, 'subgroup_hash': 1754176332075151137, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^9.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 217018985
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.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': '157464.er', 'subgroup_hash': 7393959298707098281, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 217018996
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 118098, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.N', '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': 1048434228172096594, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^9.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019007
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 118098, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.N', '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': 8699427691370023181, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019018
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 118098, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.4.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.N', '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': 3121968605997726052, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^9.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019029
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 118098, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.4.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.N', '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': 1063831612662200693, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^8.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019040
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 118098, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.4.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.N', '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': 2674999079273479536, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019044
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 78732, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.N', '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': '78732.gm', 'subgroup_hash': 2374248021734697269, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^8.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019045
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 78732, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.gf', 'subgroup_hash': 3929084963149490104, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.D_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 217019046
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 78732, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 200985897736285933, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^9.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 217019047
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 78732, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.6.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.fh', 'subgroup_hash': 3434146142367124949, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.(S_3\\times C_{18})', 'supersolvable': True, 'sylow': 0}
    • id: 217019049
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 78732, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.6.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3734587172866300600, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^8.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019050
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 78732, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.6.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.f1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.gd', 'subgroup_hash': 5608811400115508779, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.D_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 217019051
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 78732, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.6.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.g1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7160873757760835216, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 217019052
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 78732, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.6.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.h1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6580212350351596998, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^7.(C_6\\times S_3)', 'supersolvable': True, 'sylow': 0}
    • id: 217019053
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 59049, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '472392.dm.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', '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': ['F', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 753296589983015671, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^9.C_3', 'supersolvable': True, 'sylow': 3}
    • id: 217019054
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 39366, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.N', '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': 3074740580329679223, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^9.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019055
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 39366, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.N', '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': 3861506630568572065, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^8.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019056
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 39366, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7710203792183462065, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^8.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019057
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 39366, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.N', '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': 7974745215970133812, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019058
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 39366, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.N', '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': 304409011282125479, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019060
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 39366, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1636902777648887385, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.\\He_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019061
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 39366, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1.N', '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': 1265478327641712561, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^8.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019062
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 39366, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.h1.N', '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': 7268045990912006023, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^9.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019063
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 39366, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.i1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5496294864865907739, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^8.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019064
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 39366, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.j1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3019115220867921642, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^8.S_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019065
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 39366, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.k1.N', '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': 6860270392362545612, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019066
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 39366, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.12.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.l1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7990814971279222085, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.\\He_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019067
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 26244, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '26244.hy', 'subgroup_hash': 5719373199907924806, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^6.D_{18}', 'supersolvable': True, 'sylow': 0}
    • id: 217019068
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 26244, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7109115836731973803, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^8.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 217019069
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 26244, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.18.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7691326974108598723, 'subgroup_order': 26244, 'subgroup_tex': 'C_3^7.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019071
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 19683, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1635323833496094319, 'subgroup_order': 19683, 'subgroup_tex': 'C_3^8.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019072
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 19683, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5585183472077698458, 'subgroup_order': 19683, 'subgroup_tex': 'C_3^9', 'supersolvable': True, 'sylow': 0}
    • id: 217019073
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 19683, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.24.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1767525791324448265, 'subgroup_order': 19683, 'subgroup_tex': 'C_3^8.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019074
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 19683, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.24.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1106530987072792202, 'subgroup_order': 19683, 'subgroup_tex': 'C_3^8.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019075
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 13122, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8507370217109676324, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^8.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019076
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 13122, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8507370217109676324, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^8.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019077
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 13122, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8774001789895986890, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^7.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019078
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 13122, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 932967458327694242, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019079
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 13122, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.e1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6780602597602461048, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019080
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 13122, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.f1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9066563544962026841, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019082
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 13122, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.g1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5122954620802750792, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^8.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019083
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 13122, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.h1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7136980437109497153, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^7.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019084
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 13122, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.i1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5122954620802750792, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^8.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019085
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 13122, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.j1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8555866539452023048, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019086
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 13122, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.36.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.k1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7247811867517229255, 'subgroup_order': 13122, 'subgroup_tex': 'C_3^6.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019087
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 8748, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.54.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '54.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2641951499520177157, 'subgroup_order': 8748, 'subgroup_tex': 'C_3^6.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019088
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 6561, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.72.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6561.1396077', 'subgroup_hash': 7374565384238773860, 'subgroup_order': 6561, 'subgroup_tex': 'C_3^8', 'supersolvable': True, 'sylow': 0}
    • id: 217019089
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 6561, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.72.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6561.803474', 'subgroup_hash': 7189969515875716964, 'subgroup_order': 6561, 'subgroup_tex': 'C_3\\times C_3^6.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019090
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 6561, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.72.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6561.1396077', 'subgroup_hash': 7374565384238773860, 'subgroup_order': 6561, 'subgroup_tex': 'C_3^8', 'supersolvable': True, 'sylow': 0}
    • id: 217019091
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 6561, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.72.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6561.1388213', 'subgroup_hash': 3444373215498931637, 'subgroup_order': 6561, 'subgroup_tex': 'C_3^2\\times C_3^5.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019093
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 6561, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.72.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.e1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6561.710770', 'subgroup_hash': 8457121894520803633, 'subgroup_order': 6561, 'subgroup_tex': 'C_3\\times C_3^6.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019094
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 6561, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.72.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.f1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6561.1396077', 'subgroup_hash': 7374565384238773860, 'subgroup_order': 6561, 'subgroup_tex': 'C_3^8', 'supersolvable': True, 'sylow': 0}
    • id: 217019095
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 6561, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.72.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.g1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6561.263678', 'subgroup_hash': 879833930267632334, 'subgroup_order': 6561, 'subgroup_tex': 'C_3^7.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019096
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 4374, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.108.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7683652125666986601, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^7.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019097
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 4374, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.108.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.38', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7683652125666986601, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^7.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019098
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 4374, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.108.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7683652125666986601, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^7.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019099
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4374, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.108.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.38', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4248477463700871377, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^6.S_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019100
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 4374, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.108.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.e1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9119972515576778334, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^7.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019101
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 4374, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.108.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.f1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.38', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9119972515576778334, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^7.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019102
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 4374, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.108.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.g1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9119972515576778334, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^7.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 217019104
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 4374, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.108.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.h1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.38', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2464468183081493728, 'subgroup_order': 4374, 'subgroup_tex': 'C_3^6.S_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019105
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 2187, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.102', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 102, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9310', 'subgroup_hash': 812665320891796152, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^7', 'supersolvable': True, 'sylow': 0}
    • id: 217019106
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 2187, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.162', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9310', 'subgroup_hash': 812665320891796152, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^7', 'supersolvable': True, 'sylow': 0}
    • id: 217019107
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 2187, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.102', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 102, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9310', 'subgroup_hash': 812665320891796152, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^7', 'supersolvable': True, 'sylow': 0}
    • id: 217019108
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 2187, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.162', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9310', 'subgroup_hash': 812665320891796152, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^7', 'supersolvable': True, 'sylow': 0}
    • id: 217019109
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 2187, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.e1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.162', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9112', 'subgroup_hash': 18334803907992600, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^2\\times C_3^4.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019110
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 2187, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.f1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.170', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9310', 'subgroup_hash': 812665320891796152, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^7', 'supersolvable': True, 'sylow': 0}
    • id: 217019111
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 2187, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.g1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.170', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.5878', 'subgroup_hash': 8913683563257941874, 'subgroup_order': 2187, 'subgroup_tex': 'C_3\\times C_3^5.C_3', 'supersolvable': True, 'sylow': 0}
    • id: 217019112
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 2187, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.h1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.170', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9310', 'subgroup_hash': 812665320891796152, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^7', 'supersolvable': True, 'sylow': 0}
    • id: 217019113
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 2187, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.i1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.170', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.7968', 'subgroup_hash': 5146614079856121340, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^2\\times C_3^3:C_9', 'supersolvable': True, 'sylow': 0}
    • id: 217019115
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 2187, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.216.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.j1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.111', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 111, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2187.9310', 'subgroup_hash': 812665320891796152, 'subgroup_order': 2187, 'subgroup_tex': 'C_3^7', 'supersolvable': True, 'sylow': 0}
    • id: 217019116
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 1458, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.324.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '324.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.117', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 117, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1797', 'subgroup_hash': 1797, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019117
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 1458, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.324.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '324.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.39', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 39, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1797', 'subgroup_hash': 1797, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019118
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 1458, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.324.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '324.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.118', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 118, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1797', 'subgroup_hash': 1797, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019119
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1458, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.324.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '324.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.117', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 117, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1796', 'subgroup_hash': 1796, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019120
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1458, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.324.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '324.e1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.118', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 118, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1458.1796', 'subgroup_hash': 1796, 'subgroup_order': 1458, 'subgroup_tex': 'C_3^5:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019121
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 729, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.555', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 555, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3.S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019122
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 729, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.555', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 555, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3.S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019123
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 729, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.603', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 603, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019124
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 729, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.D', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.d1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.555', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 555, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3.S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019126
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 729, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.E', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.e1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.734', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 734, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019127
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 729, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.f1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.731', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 731, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['C7'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019128
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 729, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.G', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.g1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.603', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 603, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019129
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 729, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.h1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.731', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 731, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019130
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': True, 'core_order': 729, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.I', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.i1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.731', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 731, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.416', 'subgroup_hash': 416, 'subgroup_order': 729, 'subgroup_tex': 'C_3^4:C_9', 'supersolvable': True, 'sylow': 0}
    • id: 217019131
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 729, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.J', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.j1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.299', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 299, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_3^3:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019132
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': False, 'core_order': 729, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.k1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.604', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 604, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019133
      {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 19683, 'characteristic': True, 'core_order': 729, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.648.L', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '648.l1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.604', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 604, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '729.504', 'subgroup_hash': 504, 'subgroup_order': 729, 'subgroup_tex': 'C_3^6', 'supersolvable': True, 'sylow': 0}
    • id: 217019134
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 486, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.972.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '972.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '972.436', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 436, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 972, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^4:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.259', 'subgroup_hash': 259, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217019135
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': True, 'core_order': 486, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.972.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '972.b1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '972.429', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 429, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 972, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.259', 'subgroup_hash': 259, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
    • id: 217018986
      {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '472392.dm', 'ambient_counter': 91, 'ambient_order': 472392, 'ambient_tex': 'C_3^7.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 486, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '472392.dm.972.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '972.c1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '972.429', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 429, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 972, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '486.260', 'subgroup_hash': 260, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 152 matching records in this table.
    • id: 217018984
      {'ambient': '472392.dm', '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': [1271, 795, 503, 51], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 223383498153158185171252046349548996212434, 170184613510976278886462041186110401542466, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.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': '472392.dm', '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': '472392.dm'}
    • id: 217018985
      {'ambient': '472392.dm', '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.A', 'coset_action_label': None, 'count': 3, 'diagramx': [4385, -1, 8381, -1], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93405312004, 17684330597382540391211774096784, 223383498153158185171252046349548996212434, 26980883647382640810484, 4866180626571344880, 711549212774547, 148314850737164430706192434875308844853365, 170184613520122929276517489767550618585105, 9146650365332299797192399018244], 'label': '472392.dm.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': '472392.dm', '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': '157464.er'}
    • id: 217018986
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '972.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '972.C', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 3395, -1, 7354], 'generators': [526270820517725416616431696011309504, 9146650365332299797192399018244, 376610261574963, 10628380765426555680412540625193921177603, 116407477872491427463199718800047332833525, 51704033477944353408003], 'label': '472392.dm.972.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '972.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '972.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.C', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217018987
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1944.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1362, -1, 7535], 'generators': [526270820517725416616431696011309504, 10628380765426555680412540625193921177603, 10628380765425749122220858683513520301508, 10628380774572399435841703605484685849744, 20666295941918940249388752679410765888003], 'label': '472392.dm.1944.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.A', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018988
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1944.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 3323, -1, 7737], 'generators': [9147069192731485033453038186483, 526270820517725416616431696011309504, 9146650365332299797192399018244, 9147069141022586128451262566548, 10628380765426555680412540625193921177603], 'label': '472392.dm.1944.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.B', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018989
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1944.C', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2833, -1, 7687], 'generators': [526270820517725416616431696011309504, 9146650365332299797192399018244, 9147069141022586128451262566548, 10628380765426555680412540625193921177603, 9147069192726619606140308121744], 'label': '472392.dm.1944.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.C', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018990
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1944.D', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 5283, -1, 7939], 'generators': [9147069192726619940904982663107, 526270820517725416616431696011309504, 9146650365332299797192399018244, 9147069141022586128451262566548, 10628380765426555680412540625193921177603], 'label': '472392.dm.1944.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.d1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.D', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018991
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1944.E', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3813, -1, 7787], 'generators': [17683523987479404620462088192240, 9147456921273669403019911296147, 17683524039188303567577205482244, 526270820517725416616431696011309504, 10628380783109273084969692034291436057840], 'label': '472392.dm.1944.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.e1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.E', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018992
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1944.F', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 4304, -1, 7838], 'generators': [17683523987479404620462088192240, 9147456921273669403019911296147, 526270820517725416616431696011309504, 10628380783109273084969692034291436057840, 9146650365329987828909774983204], 'label': '472392.dm.1944.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.f1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.F', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018993
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1944.G', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 382, -1, 7434], 'generators': [526270820517725416616431696011309504, 9146650365332299797192399018244, 26980883647382640810484, 17684330597382540391211774096784, 10628380774572399408868240309494861933603], 'label': '472392.dm.1944.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.g1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.G', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018994
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1944.H', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 873, -1, 7484], 'generators': [10628652119101336968945826904512973418240, 526270820517725416616766635006099763, 20666822194446157246393637822539025130388, 526261674286189736370176836597907764, 10628380783109273084969692034291436057840], 'label': '472392.dm.1944.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.H', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.h1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.H', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018995
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1944.I', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6263, -1, 8040], 'generators': [10628907044783140445054008292371757226388, 10628652119101336968945826904512973418240, 20666822194446157246393637822539025130388, 526261674286189736370176836597907764, 10628380783109273084969692034291436057840], 'label': '472392.dm.1944.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.I', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.i1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.I', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018996
      {'ambient': '472392.dm', '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': '52488.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1435, -1, 840], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 212138873226789695283397513335233676405265, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.4.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.a1.N', 'projective_image': '472392.dm', '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': '52488.fu'}
    • id: 217018997
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1944.J', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2342, -1, 7636], 'generators': [271371359111858932388852836708416000, 526279357391401518310358976206937748, 10628652119101336941969809814634920038404, 10628380774572399435841703605484685849744, 10628380783110079640918481991244003334964], 'label': '472392.dm.1944.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.J', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.j1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.J', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217018998
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1944.K', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1853, -1, 7586], 'generators': [271371359111910636422330432225280004, 526279357391401518310358976206937748, 9147456921273669403019911296147, 4865804109802137744, 10628380774572399408868240309494861933603], 'label': '472392.dm.1944.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.K', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.k1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.K', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217018999
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1944.L', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 4794, -1, 7889], 'generators': [526270820517725416616431696011309504, 9146650365332299797192399018244, 17684330597382540391211774096784, 51706588401582205639204, 10628380774572399408868240309494861933603], 'label': '472392.dm.1944.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.L', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.l1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.L', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019000
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1944.M', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6754, -1, 8091], 'generators': [9147456921273669403019911296147, 526270820517725416616431696011309504, 10628380783109273084969692034291436057840, 51706588401582205639204, 17683524014457976299562104966964], 'label': '472392.dm.1944.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.M', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.m1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.M', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019001
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '1944.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1944.N', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5774, -1, 7990], 'generators': [51704033854554607725364, 526270820517725416616431696011309504, 9146650365332299797192399018244, 17684330597382540391211774096784, 10628380774572399408868240309494861933603], 'label': '472392.dm.1944.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1944.N', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.n1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.N', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019002
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '2916.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.J', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2916.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 597, -1, 8164], 'generators': [526261674286189736370176836597907764, 271371359111910641288134542027417748, 202100431788622217966490694615646635125265, 10628652119101336993676154883996328064148, 10628380783109273084969692034291436057840], 'label': '472392.dm.2916.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2916.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2916.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2916.A', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
    • id: 217019003
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1817, -1, 8388], 'generators': [526270820517725416616431696011309504, 10628380765426555680412540625193921177603, 10628380774572399435841703605484685849744, 10628380774572399408870551566321678506484], 'label': '472392.dm.5832.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.A', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019004
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 3777, -1, 8590], 'generators': [10628907027099616484555487653870021190960, 9147456921273669403019911296147, 10628652119101336941972121071461816409844, 10628380774572399435841703605484685849744], 'label': '472392.dm.5832.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.B', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019005
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.C', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 4268, -1, 8641], 'generators': [526270820517725416616431696011309504, 9146650365332299797192399018244, 9147069141022586128451262566548, 10628380765426555680412540625193921177603], 'label': '472392.dm.5832.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.C', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019006
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.H', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.D', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 836, -1, 8287], 'generators': [20666822212130487868504194224683767943203, 10628907044783559274706062211128033965604, 10628652128248406134696429043990610128784, 20666295941919746807585544426683070611760], 'label': '472392.dm.5832.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.d1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.D', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019007
      {'ambient': '472392.dm', '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': '52488.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '4.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2266, -1, 925], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 169892903214970987854598249749830968567414, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.4.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.b1.N', 'projective_image': '472392.dm', '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': '52488.fy'}
    • id: 217019008
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.E', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6228, -1, 8843], 'generators': [17683523987479404620462088192240, 9147456921273669403019911296147, 526270820517725416616431696011309504, 10628380783109273084969692034291436057840], 'label': '472392.dm.5832.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.e1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.E', 'subgroup_fusion': None, 'weyl_group': '8.5'}
    • id: 217019009
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.F', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1327, -1, 8337], 'generators': [10628652119101336968945826904512973418240, 526261674286189736370176836597907764, 10628380783109273084969692034291436057840, 10628380774572399408870551566321678506484], 'label': '472392.dm.5832.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.f1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.F', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019010
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.G', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 3287, -1, 8540], 'generators': [10628907044783140445054008292371757226388, 10628652119101336968945826904512973418240, 526261674286189736370176836597907764, 10628380783109273084969692034291436057840], 'label': '472392.dm.5832.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.g1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.G', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019011
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.H', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2307, -1, 8438], 'generators': [10628907044783140445056563216090560601604, 526279357391401518310358976206937748, 10628380774572399435841703605484685849744, 10628380783110079640918481991244003334964], 'label': '472392.dm.5832.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.H', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.h1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.H', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019012
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.I', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6719, -1, 8893], 'generators': [526279357391401518310358976206937748, 10628652119101336941969809814634920038404, 10628380774572399435841703605484685849744, 10628380783110079640918481991244003334964], 'label': '472392.dm.5832.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.I', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.i1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.I', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019013
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.J', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 5738, -1, 8792], 'generators': [526270820517725416616431696011309504, 9146650365332299797192399018244, 10628380765426555680412540625193921177603, 51704033477944353408003], 'label': '472392.dm.5832.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.J', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.j1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.J', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019014
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.K', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 347, -1, 8236], 'generators': [271371359111910638976877715247168244, 526279357391401518310358976206937748, 9147456921273669403019911296147, 10628380774572399408868240309494861933603], 'label': '472392.dm.5832.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.K', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.k1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.K', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019015
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '5832.L', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 5248, -1, 8742], 'generators': [9147456921273669403019911296147, 526270820517725416616431696011309504, 10628380783109273084969692034291436057840, 51706588401582205639204], 'label': '472392.dm.5832.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.L', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.l1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.L', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019016
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.M', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2797, -1, 8489], 'generators': [526270820517725416616431696011309504, 9146650365332299797192399018244, 17684330597382540391211774096784, 10628380774572399408868240309494861933603], 'label': '472392.dm.5832.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.M', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.m1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.M', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019017
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '5832.N', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '5832.N', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4757, -1, 8691], 'generators': [526261674286189736370176836597907764, 271371359111910641288134542027417748, 10628652119101336993676154883996328064148, 10628380783109273084969692034291436057840], 'label': '472392.dm.5832.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5832.N', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '5832.n1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5832.N', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019018
      {'ambient': '472392.dm', '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': '52488.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '4.C', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 4077, -1, 1112], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 223675734719374217315731343625286326554855, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.4.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.c1.N', 'projective_image': '472392.dm', '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': '52488.gk'}
    • id: 217019019
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '17496.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 347, -1, 8944], 'generators': [10628907027099616484555487653870021190960, 9147456921273669403019911296147, 10628380774572399435841703605484685849744], 'label': '472392.dm.17496.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.A', 'subgroup_fusion': None, 'weyl_group': '8.5'}
    • id: 217019020
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.H', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '17496.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 836, -1, 8994], 'generators': [20666822212130487868504194224683767943203, 10628907044783559274706062211128033965604, 20666567286448684340684559008104405139904], 'label': '472392.dm.17496.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.B', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019021
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.H', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '17496.C', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2307, -1, 9146], 'generators': [20666822203593226439125122521308369005508, 9147069141022586128451262566548, 271371359530688584442436573075417603], 'label': '472392.dm.17496.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.C', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019022
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '17496.D', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4757, -1, 9399], 'generators': [10628652119101336968945826904512973418240, 526261674286189736370176836597907764, 10628380783109273084969692034291436057840], 'label': '472392.dm.17496.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.d1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.D', 'subgroup_fusion': None, 'weyl_group': '8.5'}
    • id: 217019023
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '17496.E', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1327, -1, 9045], 'generators': [9147069192731485033453038186483, 10628907036247073405829157056889932487107, 271353676006674126709427479550135044], 'label': '472392.dm.17496.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.e1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.E', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019024
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '17496.F', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5248, -1, 9449], 'generators': [526279357391401518310358976206937748, 10628380774572399435841703605484685849744, 10628380783110079640918481991244003334964], 'label': '472392.dm.17496.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.f1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.F', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019025
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '17496.G', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 3287, -1, 9247], 'generators': [526270820517725416616431696011309504, 10628380765426555680412540625193921177603, 17683524014457976299562104966964], 'label': '472392.dm.17496.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.g1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.G', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019026
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '17496.H', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1817, -1, 9096], 'generators': [526279357391401518310358976206937748, 9147456921273669403019911296147, 10628380774572399408868240309494861933603], 'label': '472392.dm.17496.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.H', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.h1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.H', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019027
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '17496.I', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4268, -1, 9348], 'generators': [9147456921273669403019911296147, 526270820517725416616431696011309504, 10628380783109273084969692034291436057840], 'label': '472392.dm.17496.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.I', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.i1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.I', 'subgroup_fusion': None, 'weyl_group': '8.5'}
    • id: 217019028
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '17496.J', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2797, -1, 9196], 'generators': [526261674286189736370176836597907764, 10628652119101336993676154883996328064148, 10628380783109273084969692034291436057840], 'label': '472392.dm.17496.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.J', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.j1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.J', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019029
      {'ambient': '472392.dm', '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': '52488.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.D', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 669, -1, 761], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 212437102276031507089328050973352030649534, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.4.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.d1.N', 'projective_image': '472392.dm', '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': '52488.go'}
    • id: 217019030
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '17496.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '17496.K', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3777, -1, 9298], 'generators': [271371359111910638976877715247168244, 526279357391401518310358976206937748, 10628380783110079640918481991244003334964], 'label': '472392.dm.17496.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '17496.K', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '17496.k1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '17496.K', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019031
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '52488.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.C', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '52488.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1291, -1, 9601], 'generators': [20666822203593226439125122521308369005508, 9147069141022586128451262566548], 'label': '472392.dm.52488.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '52488.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '52488.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52488.A', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 217019032
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '52488.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '52488.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1781, -1, 9651], 'generators': [10628907036247073405829157056889932487107, 271353676006674126709427479550135044], 'label': '472392.dm.52488.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '52488.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '52488.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52488.B', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 217019033
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '52488.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '52488.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3251, -1, 9803], 'generators': [20666822212130487868504194224683767943203, 20666567286448684340684559008104405139904], 'label': '472392.dm.52488.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '52488.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '52488.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52488.C', 'subgroup_fusion': None, 'weyl_group': '6.1'}
    • id: 217019034
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '52488.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '52488.D', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2271, -1, 9702], 'generators': [10628907027099616484555487653870021190960, 9147456921273669403019911296147], 'label': '472392.dm.52488.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '52488.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '52488.d1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52488.D', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 217019035
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '52488.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.H', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '52488.E', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 801, -1, 9550], 'generators': [20666822203593226439125122521308369005508, 271362822238236785284029392582745844], 'label': '472392.dm.52488.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '52488.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '52488.e1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52488.E', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019036
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '52488.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.D', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '52488.F', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2762, -1, 9752], 'generators': [526261674286189736370176836597907764, 10628380783109273084969692034291436057840], 'label': '472392.dm.52488.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '52488.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '52488.f1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52488.F', 'subgroup_fusion': None, 'weyl_group': '4.2'}
    • id: 217019037
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '52488.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '52488.G', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 310, -1, 9500], 'generators': [526279357391401518310358976206937748, 10628380783110079640918481991244003334964], 'label': '472392.dm.52488.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '52488.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '52488.g1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '52488.G', 'subgroup_fusion': None, 'weyl_group': '12.4'}
    • id: 217019038
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '59049.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': '472392.a1', 'coset_action_label': None, 'count': 19683, 'diagramx': None, 'generators': [202100686714304440247520601942778341026721, 10336942115812731057098807400812135435069, 287499222733633191137419186595186695904639], 'label': '472392.dm.59049.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '59049.a1', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '59049.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 217019039
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '157464.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '157464.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 281, -1, 9850], 'generators': [20666822212130487868504194224683767943203], 'label': '472392.dm.157464.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '157464.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '157464.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '157464.A', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 217019040
      {'ambient': '472392.dm', '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': '472392.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.E', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3246, -1, 1026], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.4.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.e1.N', 'projective_image': '472392.dm', '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': '472392.dm'}
    • id: 217019041
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '157464.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '157464.B', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 711, -1, 9895], 'generators': [20666822203593226439125122521308369005508], 'label': '472392.dm.157464.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '157464.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '157464.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '157464.B', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 217019042
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '157464.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '157464.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1141, -1, 9939], 'generators': [10628907036247073405829157056889932487107], 'label': '472392.dm.157464.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '157464.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '157464.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '157464.C', 'subgroup_fusion': None, 'weyl_group': '2.1'}
    • id: 217019043
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '472392.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '472392.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 281, -1, 9984], 'generators': [], 'label': '472392.dm.472392.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '472392.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '472392.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '472392.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
    • id: 217019044
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '6.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 758, -1, 1204], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93405312004, 17684330597382540391211774096784, 169892903214970987854598250126615506800598, 223383498153158185171252046349548996212434, 26980883647382640810484, 4866180626571344880, 711549212774547, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.6.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.A', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217019045
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1865, -1, 1318], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 169892903214970987854598249749830968567414, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 223383498153158185171252046349549039677493, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.B', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217019046
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '6.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5457, -1, 1688], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 116407732780489706927103034814726615972645, 287499222724486540826041233322991915203915, 26980883647382640810484, 4866180626571344880, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.6.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.C', 'subgroup_fusion': None, 'weyl_group': '52488.gd'}
    • id: 217019047
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '6.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.D', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 3641, -1, 1501], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 170184613510976278886462041186110401542466, 223675734728520867602378725962654898622135, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.6.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.d1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.D', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217019048
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '2.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2.A', 'coset_action_label': None, 'count': 1, 'diagramx': [1143, 729, 1558, 159], 'generators': [10628380774572399408868240309494861933603, 169892903214970987854598249749830968567414, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 223383498153158185171252046349548996212434, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.2.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.A', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217019049
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '6.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '472392.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '6.E', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 4561, -1, 1596], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 212437357184028980022013147254530186195278, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.6.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.e1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.E', 'subgroup_fusion': None, 'weyl_group': '472392.dm'}
    • id: 217019050
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '6.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '157464.B', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '6.F', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2815, -1, 1416], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 223383498153158185171252046349549039677493, 170184613510976278886462041186110401542466, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.6.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.f1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.F', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217019051
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '6.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '472392.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '6.G', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 7627, -1, 1912], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 17684330597382540391211774096784, 174436496880, 376610261574963, 223383498153158185171252046349548996212434, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.6.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.g1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.G', 'subgroup_fusion': None, 'weyl_group': '472392.dm'}
    • id: 217019052
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '6.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '472392.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '6.H', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 6449, -1, 1791], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 223383498153158185171252046349549039677493, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.6.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.H', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.h1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.H', 'subgroup_fusion': None, 'weyl_group': '472392.dm'}
    • id: 217019053
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 544, -1, 2008], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.8.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '80000.ww'}
    • id: 217019054
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.J', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1219, -1, 2147], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 212138873226789695283397513335233676405265, 4866180626571344880, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.12.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.A', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
    • id: 217019055
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 7018, -1, 2745], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93405312004, 17684330597382540391211774096784, 212138346955968758730581711332418946165265, 26980883647382640810484, 4866180626571344880, 711549212774547, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.12.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.B', 'subgroup_fusion': None, 'weyl_group': '52488.fu'}
    • id: 217019056
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 7693, -1, 2814], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 212138873235325762297894348936218313845265, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.12.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.C', 'subgroup_fusion': None, 'weyl_group': '52488.fu'}
    • id: 217019057
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.D', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 3030, -1, 2334], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 17684330597382540391211774096784, 174436496880, 376610261574963, 223383498153158185171252046349548996212434, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.12.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.d1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.D', 'subgroup_fusion': None, 'weyl_group': '52488.fy'}
    • id: 217019058
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.E', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 4011, -1, 2435], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93405312004, 17684330597382540391211774096784, 223383498153158185171252046349548996212434, 26980883647382640810484, 4866180626571344880, 711549212774547, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.12.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.e1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.E', 'subgroup_fusion': None, 'weyl_group': '52488.fy'}
    • id: 217019059
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '2.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '2.B', 'coset_action_label': None, 'count': 1, 'diagramx': [2874, 1619, 2456, 251], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 223675734719374217315731343625286326554855, 93485226483, 17684330597382540391211774096784, 170184613510976278886462041186110401542466, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.2.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.B', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217019060
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.F', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 2050, -1, 2233], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 169892903214970987854598249749830968567414, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.12.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.f1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.F', 'subgroup_fusion': None, 'weyl_group': '52488.fy'}
    • id: 217019061
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.G', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 8368, -1, 2884], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 223675734719374217315731343625286326554855, 17684330597382540391211774096784, 174436496880, 376610261574963, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.12.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.g1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.G', 'subgroup_fusion': None, 'weyl_group': '52488.gk'}
    • id: 217019062
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.H', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 544, -1, 2077], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 116407732780489706927103034814726615972645, 26980883647382640810484, 4866180626571344880, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.12.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.H', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.h1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.H', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217019063
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.I', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 9043, -1, 2954], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 223675734728520867602378725962654898622135, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.12.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.I', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.i1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.I', 'subgroup_fusion': None, 'weyl_group': '52488.gk'}
    • id: 217019064
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.F', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.J', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 9719, -1, 3023], 'generators': [10628380774572399408868240309494861933603, 212437357184028980022013147254530186195278, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.12.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.J', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.j1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.J', 'subgroup_fusion': None, 'weyl_group': '52488.go'}
    • id: 217019065
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '472392.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '12.K', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 5099, -1, 2547], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 17684330597382540391211774096784, 174436496880, 376610261574963, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.12.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.K', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.k1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.K', 'subgroup_fusion': None, 'weyl_group': '472392.dm'}
    • id: 217019066
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '12.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '472392.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '12.L', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 6187, -1, 2659], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.12.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.L', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '12.l1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.L', 'subgroup_fusion': None, 'weyl_group': '472392.dm'}
    • id: 217019067
      {'ambient': '472392.dm', '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': '157464.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '18.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 604, -1, 3099], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 17684330597382540391211774096784, 169892903214970987854598250126615506800598, 26980883647382640810484, 234011878918583934241766316296715796046034, 4866180626571344880, 711549212774547, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.18.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '18.a1.N', 'projective_image': '472392.dm', '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}
    • id: 217019068
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '18.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.C', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '18.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2199, -1, 3264], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 287499222724486540826041233322991915203915, 26980883647382640810484, 4866180626571344880, 116407732771952833302703062731617516385525, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.18.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '18.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.B', 'subgroup_fusion': None, 'weyl_group': '52488.gd'}
    • id: 217019069
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '18.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '472392.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '18.C', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1398, -1, 3181], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 255296591551655751594003763412586989301363, 526270820517725416616431696011309504, 255296591551655751593998897273712548955764, 17684330597382540391211774096784, 148314850737164430706192434540637532088389, 26980883647382640810484, 170184613520122929276517489767550618585105, 9146650365332299797192399018244], 'label': '472392.dm.18.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '18.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '18.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.C', 'subgroup_fusion': None, 'weyl_group': '472392.dm'}
    • id: 217019070
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '2.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': '2.C', 'coset_action_label': None, 'count': 1, 'diagramx': [4733, 2576, 3421, 350], 'generators': [298500669107992362519262758492590365561, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 212437102276031507089328050973352030649534, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.2.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.C', 'subgroup_fusion': None, 'weyl_group': '472392.dm'}
    • id: 217019071
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '24.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.E', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '24.A', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 1715, -1, 3460], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 17684330597382540391211774096784, 174436496880, 376610261574963, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.24.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.A', 'subgroup_fusion': None, 'weyl_group': '80000.ww'}
    • id: 217019072
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '24.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 454, -1, 3330], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.24.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.B', 'subgroup_fusion': None, 'weyl_group': '24.14'}
    • id: 217019073
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '24.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1040, -1, 3391], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93405312004, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 711549212774547, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.24.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.C', 'subgroup_fusion': None, 'weyl_group': '80000.ww'}
    • id: 217019074
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '24.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.E', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.D', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2390, -1, 3530], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.24.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '24.d1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.D', 'subgroup_fusion': None, 'weyl_group': '80000.ww'}
    • id: 217019075
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '36.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.J', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2253, -1, 3776], 'generators': [376784574566643, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 191472305931194748359884606487175595125265, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 711549212774547, 9146650365332299797192399018244], 'label': '472392.dm.36.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.a1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.A', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
    • id: 217019076
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '36.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1944.J', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.B', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 2929, -1, 3846], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 93485226483, 212138873235325762297894348936218313845265, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.36.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.b1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.B', 'subgroup_fusion': None, 'weyl_group': '1944.2342'}
    • id: 217019077
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '36.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.B', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.C', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 8194, -1, 4389], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 17684330597382540391211774096784, 26980883647382640810484, 4866180626571344880, 711549212774547, 148314850737164430706192434875308844853365, 212138601863967038246193926628884579445265, 9146650365332299797192399018244], 'label': '472392.dm.36.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.c1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.C', 'subgroup_fusion': None, 'weyl_group': '52488.fu'}
    • id: 217019078
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '36.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.D', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 6575, -1, 4222], 'generators': [376784574566643, 10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 17684330597382540391211774096784, 223383498153158185171252046349548996212434, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.36.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.d1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.D', 'subgroup_fusion': None, 'weyl_group': '52488.fy'}
    • id: 217019079
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '36.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.E', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 7429, -1, 4310], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 17684330597382540391211774096784, 376610261574963, 26980883647382640810484, 244049794085930475030585349024595396177014, 4866180626571344880, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.36.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.e1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.E', 'subgroup_fusion': None, 'weyl_group': '52488.fy'}
    • id: 217019080
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '36.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.F', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 5719, -1, 4133], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 17684330597382540391211774096784, 26980883647382640810484, 234011878918583934241766316296715796046034, 4866180626571344880, 711549212774547, 148314850737164430706192434875308844853365, 9146650365332299797192399018244], 'label': '472392.dm.36.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.F', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.f1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.F', 'subgroup_fusion': None, 'weyl_group': '52488.fy'}
    • id: 217019081
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '2.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '2.D', 'coset_action_label': None, 'count': 2, 'diagramx': [6881, 3682, 4536, 464], 'generators': [10628380774572399408868240309494861933603, 169892903214970987854598249749830968567414, 526270820517725416616431696011309504, 93485226483, 17684330597382540391211774096784, 212437102276031507089328050973352030649534, 26980883647382640810484, 4866180626571344880, 148314850737164430706192434875308844853365, 43591107, 711468305095200, 9146650365332299797192399018244], 'label': '472392.dm.2.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.D', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217019082
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '36.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '5832.D', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.G', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 3604, -1, 3915], 'generators': [376784574566643, 526270820517725416616431696011309504, 9146650365332299797192399018244, 376610261574963, 26980883647382640810484, 17684330597382540391211774096784, 116407732780489706927103034814726615972645, 4866180626571344880, 10628380774572399408868240309494861933603], 'label': '472392.dm.36.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.G', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.g1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.G', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 217019083
      {'ambient': '472392.dm', 'aut_centralizer_order': None, 'aut_label': '36.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '52488.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '36.H', 'coset_action_label': None, 'count': 2, 'diagramx': [-1, 4955, -1, 4054], 'generators': [10628380774572399408868240309494861933603, 526270820517725416616431696011309504, 255296591551655751594003763412586989301363, 255296591551655751593998897273712548955764, 17684330597382540391211774096784, 148314850737164430706192434540637532088389, 26980883647382640810484, 170184613520122929276517489767550618585105, 9146650365332299797192399018244], 'label': '472392.dm.36.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.H', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.h1.N', 'projective_image': '472392.dm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.H', 'subgroup_fusion': None, 'weyl_group': '52488.gk'}