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  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [18, 12, 36, 12], 'aut_gens': [[244050880369023955532401898366136741200668, 297836716282674354632265147391380864733439, 371989532658154783760856509160051209468852], [116698076512707024490563436850920521244226, 308170127269697832572559729010210166959173, 361659907452150912008539939729998801997467], [159563821392093273817149243553580007074399, 95739815439710224363804009597159013809228, 106366566326727483880687395889058934529917], [371991433817613907939595806834347768048242, 297535516318980987423612988807932266701174, 308168786151247430076429023192930721488514], [307872441842612155838820698641199481749612, 361658548982365794838147758440567939193000, 244050065439601433060822742973121355624814]], 'aut_group': None, 'aut_hash': 1591828275226491776, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 51018336, 'aut_permdeg': 1026, 'aut_perms': 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'aut_phi_ratio': 162.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 54, 1, 1], [2, 486, 2, 1], [2, 729, 1, 2], [2, 4374, 1, 1], [2, 6561, 1, 1], [3, 2, 2, 1], [3, 4, 1, 3], [3, 8, 1, 2], [3, 8, 2, 2], [3, 16, 1, 1], [3, 36, 1, 1], [3, 72, 1, 2], [3, 72, 9, 1], [3, 144, 1, 1], [3, 144, 9, 1], [3, 324, 1, 1], [3, 648, 6, 1], [3, 1296, 3, 1], [3, 1296, 6, 1], [4, 13122, 2, 1], [6, 108, 1, 3], [6, 108, 2, 1], [6, 216, 1, 2], [6, 216, 2, 1], [6, 972, 1, 1], [6, 972, 2, 2], [6, 1458, 2, 1], [6, 1944, 1, 1], [6, 1944, 2, 1], [6, 1944, 9, 1], [6, 2916, 1, 3], [6, 8748, 1, 2], [6, 8748, 2, 1], [6, 17496, 1, 1], [6, 17496, 6, 1], [6, 26244, 1, 2], [9, 36, 3, 1], [9, 36, 9, 1], [9, 72, 3, 2], [9, 72, 9, 1], [9, 144, 3, 1], [9, 162, 6, 1], [9, 324, 3, 1], [9, 324, 6, 1], [9, 648, 3, 3], [9, 648, 9, 1], [9, 648, 18, 1], [9, 1296, 9, 1], [12, 26244, 2, 1], [18, 108, 9, 1], [18, 216, 9, 1], [18, 972, 3, 1], [18, 972, 6, 3], [18, 972, 9, 1], [18, 1458, 6, 1], [18, 1944, 3, 2], [18, 1944, 9, 1], [18, 1944, 18, 1], [18, 2916, 3, 2], [18, 2916, 6, 1], [18, 2916, 9, 1], [18, 5832, 3, 2], [18, 8748, 3, 1], [18, 8748, 6, 2], [18, 17496, 3, 1], [36, 26244, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^6.C_3^4.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': 1591828275226491776, 'autcentquo_nilpotent': False, 'autcentquo_order': 51018336, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^6.C_3^5.C_6^2.C_2^3', 'cc_stats': [[1, 1, 1], [2, 54, 1], [2, 486, 2], [2, 729, 2], [2, 4374, 1], [2, 6561, 1], [3, 2, 2], [3, 4, 3], [3, 8, 6], [3, 16, 1], [3, 36, 1], [3, 72, 11], [3, 144, 10], [3, 324, 1], [3, 648, 6], [3, 1296, 9], [4, 13122, 2], [6, 108, 5], [6, 216, 4], [6, 972, 5], [6, 1458, 2], [6, 1944, 12], [6, 2916, 3], [6, 8748, 4], [6, 17496, 7], [6, 26244, 2], [9, 36, 12], [9, 72, 15], [9, 144, 3], [9, 162, 6], [9, 324, 9], [9, 648, 36], [9, 1296, 9], [12, 26244, 2], [18, 108, 9], [18, 216, 9], [18, 972, 30], [18, 1458, 6], [18, 1944, 33], [18, 2916, 21], [18, 5832, 6], [18, 8748, 15], [18, 17496, 3], [36, 26244, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '944784.rx', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 14, 'conjugacy_classes_known': True, 'counter': 466, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 54, 1, 1], [2, 486, 1, 2], [2, 729, 1, 2], [2, 4374, 1, 1], [2, 6561, 1, 1], [3, 2, 1, 2], [3, 4, 1, 3], [3, 8, 1, 6], [3, 16, 1, 1], [3, 36, 1, 1], [3, 72, 1, 11], [3, 144, 1, 10], [3, 324, 1, 1], [3, 648, 1, 6], [3, 1296, 1, 9], [4, 13122, 1, 2], [6, 108, 1, 5], [6, 216, 1, 4], [6, 972, 1, 5], [6, 1458, 1, 2], [6, 1944, 1, 12], [6, 2916, 1, 3], [6, 8748, 1, 4], [6, 17496, 1, 7], [6, 26244, 1, 2], [9, 36, 3, 4], [9, 72, 3, 5], [9, 144, 3, 1], [9, 162, 3, 2], [9, 324, 3, 3], [9, 648, 3, 12], [9, 1296, 3, 3], [12, 26244, 1, 2], [18, 108, 3, 3], [18, 216, 3, 3], [18, 972, 3, 10], [18, 1458, 3, 2], [18, 1944, 3, 11], [18, 2916, 3, 7], [18, 5832, 3, 2], [18, 8748, 3, 5], [18, 17496, 3, 1], [36, 26244, 3, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [10, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 18], [48, 1, 9], [72, 1, 18], [144, 1, 12]], 'familial': False, 'frattini_label': '729.504', 'frattini_quotient': '1296.3528', 'hash': 4214627173336113295, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [36, 4, 6], 'inner_gens': [[244050880369023955532401898366136741200668, 180229591054657757954706805809947997895946, 307867552619483051164819294722402277621709], [234009994187128676174962741623002502470158, 297836716282674354632265147391380864733439, 287204516031430505936748878732044555615436], [52873544325509173749300093954575351296707, 361363053052184771814282767790243654249845, 371989532658154783760856509160051209468852]], 'inner_hash': 4214627173336113295, 'inner_nilpotent': False, 'inner_order': 944784, 'inner_split': None, 'inner_tex': 'C_3^6.S_3^2:S_3^2', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 10], [4, 14], [8, 12], [12, 52], [16, 1], [18, 24], [24, 52], [36, 46], [48, 13], [72, 84], [144, 18]], 'label': '944784.rx', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^6.S3^2:S3^2', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 90, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 334, 'number_divisions': 182, 'number_normal_subgroups': 47, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 944784, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 13419], [3, 18224], [4, 26244], [6, 251208], [9, 40824], [12, 52488], [18, 384912], [36, 157464]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [3, 6, 3], 'outer_gen_pows': [20666822203593226439125122521227417770387, 298500476807218563126693594451883025211, 191468239887785193731351893401426515626803], 'outer_gens': [[244050608832821975934962137751646970679163, 42546906890768935849334701416122070137545, 96033155211515977039322372550327217062212], [307872441842612155838820698641199481749612, 361658548982365794838147758440567939193000, 244050065439601433060822742973121355624814], [297539030727396874833311957404280989356964, 244343660283603373721722495989509740539025, 159555961309457492391578870081030219217115]], 'outer_group': '54.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 54, 'outer_permdeg': 18, 'outer_perms': [1989816157143936, 1535593698060819, 5947020276487111], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3\\times C_3^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 10], [4, 14], [8, 12], [12, 4], [16, 1], [24, 22], [36, 20], [48, 10], [54, 8], [72, 22], [108, 14], [144, 10], [216, 24], [432, 3]], 'representations': {'PC': {'code': '110935153570703862790360226702015346895914113911266049559080125977082826926620622182845277371577384672368192817900802256549532295051771683686873446863630629212575071048278934753370089582406263544618747623377413779479160410461699435256787083547875926776680703420739142744466849743152729230734418935936602178551222120903951815570587676194842363019044166193511379109378248307402373843711', 'gens': [1, 2, 4, 6, 9, 11, 12, 13, 14], 'pres': [14, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 11229624, 9342425, 71, 27344858, 9609168, 32192163, 445217, 4727719, 157, 34324084, 7894338, 12943172, 1837140, 61396277, 9645067, 9106809, 3480167, 1483585, 243, 36070278, 31116980, 7341802, 2447304, 2509058, 384, 870919, 217749, 24227, 8113, 96090632, 58586998, 2898540, 1007042, 313048, 18222, 498, 60489, 60503, 272197, 90771, 15199, 79767082, 39850296, 3891926, 349324, 99858, 124820, 5666, 64665227, 55847257, 84992556, 46427498, 38584768, 3249846, 828896, 2083618, 619260, 19780, 61725915]}, 'Perm': {'d': 36, 'gens': [371989532658154783760856509160051209468852, 244050880369023955532401898366136741200668, 297836716282674354632265147391380864733439]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 243, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.S_3^2:S_3^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_conj_classes • Show schema
    Showing the first 100 of 334 matching records in this table.
    • id: 170339360
      {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 466, 'group_order': 944784, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
    • id: 170339471
      {'aut_label': '2A', 'centralizer': '54.G', 'counter': 2, 'group_counter': 466, 'group_order': 944784, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1637963881973414418113513221708426052, 'size': 54}
    • id: 170339582
      {'aut_label': '2B', 'centralizer': None, 'counter': 3, 'group_counter': 466, 'group_order': 944784, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 223681183754237170302272360965483247430001, 'size': 486}
    • id: 170339628
      {'aut_label': '2B', 'centralizer': None, 'counter': 4, 'group_counter': 466, 'group_order': 944784, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 308169041215544993450864558929054180227574, 'size': 486}
    • id: 170339639
      {'aut_label': '2D', 'centralizer': None, 'counter': 5, 'group_counter': 466, 'group_order': 944784, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 84493832711742863417578583728232511482852, 'size': 729}
    • id: 170339650
      {'aut_label': '2E', 'centralizer': None, 'counter': 6, 'group_counter': 466, 'group_order': 944784, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 201803017476481539003308832141300960089994, 'size': 729}
    • id: 170339661
      {'aut_label': '2F', 'centralizer': None, 'counter': 7, 'group_counter': 466, 'group_order': 944784, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 212435735684145667973728756031328148869115, 'size': 4374}
    • id: 170339672
      {'aut_label': '2G', 'centralizer': None, 'counter': 8, 'group_counter': 466, 'group_order': 944784, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 127947055272041756159723572872714814941835, 'size': 6561}
    • id: 170339683
      {'aut_label': '3A', 'centralizer': '2.A', 'counter': 9, 'group_counter': 466, 'group_order': 944784, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 10628907036246685625578073782240332522387, 'size': 2}
    • id: 170339361
      {'aut_label': '3A', 'centralizer': '2.A', 'counter': 10, 'group_counter': 466, 'group_order': 944784, 'label': '3B', 'order': 3, 'powers': [10, 1], 'representative': 20666822212130100088253110950034167978483, 'size': 2}
    • id: 170339372
      {'aut_label': '3C', 'centralizer': '4.F', 'counter': 11, 'group_counter': 466, 'group_order': 944784, 'label': '3C', 'order': 3, 'powers': [11, 1], 'representative': 526261674673969987453451486197943044, 'size': 4}
    • id: 170339383
      {'aut_label': '3D', 'centralizer': '4.A', 'counter': 12, 'group_counter': 466, 'group_order': 944784, 'label': '3D', 'order': 3, 'powers': [12, 1], 'representative': 271353676394454377792702129150099764, 'size': 4}
    • id: 170339394
      {'aut_label': '3E', 'centralizer': '4.H', 'counter': 13, 'group_counter': 466, 'group_order': 944784, 'label': '3E', 'order': 3, 'powers': [13, 1], 'representative': 10628907044783947054957145485777634000884, 'size': 4}
    • id: 170339405
      {'aut_label': '3F', 'centralizer': '8.D', 'counter': 14, 'group_counter': 466, 'group_order': 944784, 'label': '3F', 'order': 3, 'powers': [14, 1], 'representative': 17683523987479404620462088192240, 'size': 8}
    • id: 170339416
      {'aut_label': '3G', 'centralizer': '8.D', 'counter': 15, 'group_counter': 466, 'group_order': 944784, 'label': '3G', 'order': 3, 'powers': [15, 1], 'representative': 271371359918441857197322591238292004, 'size': 8}
    • id: 170339427
      {'aut_label': '3G', 'centralizer': '8.D', 'counter': 16, 'group_counter': 466, 'group_order': 944784, 'label': '3H', 'order': 3, 'powers': [16, 1], 'representative': 526279357810177215774797217734864883, 'size': 8}
    • id: 170339438
      {'aut_label': '3I', 'centralizer': '8.D', 'counter': 17, 'group_counter': 466, 'group_order': 944784, 'label': '3I', 'order': 3, 'powers': [17, 1], 'representative': 20666567295595334703766545046600921197508, 'size': 8}
    • id: 170339449
      {'aut_label': '3J', 'centralizer': '8.E', 'counter': 18, 'group_counter': 466, 'group_order': 944784, 'label': '3J', 'order': 3, 'powers': [18, 1], 'representative': 10628652119101336968945826904512973382960, 'size': 8}
    • id: 170339460
      {'aut_label': '3J', 'centralizer': '8.E', 'counter': 19, 'group_counter': 466, 'group_order': 944784, 'label': '3K', 'order': 3, 'powers': [19, 1], 'representative': 17684330570401657831907612774644, 'size': 8}
    • id: 170339472
      {'aut_label': '3L', 'centralizer': '16.a1', 'counter': 20, 'group_counter': 466, 'group_order': 944784, 'label': '3L', 'order': 3, 'powers': [20, 1], 'representative': 271362822657012478125619053936813507, 'size': 16}
    • id: 170339483
      {'aut_label': '3M', 'centralizer': '36.BA', 'counter': 21, 'group_counter': 466, 'group_order': 944784, 'label': '3M', 'order': 3, 'powers': [21, 1], 'representative': 51704033854380214809840, 'size': 36}
    • id: 170339494
      {'aut_label': '3N', 'centralizer': '72.S', 'counter': 22, 'group_counter': 466, 'group_order': 944784, 'label': '3N', 'order': 3, 'powers': [22, 1], 'representative': 20666822212130487868501882967776000089840, 'size': 72}
    • id: 170339505
      {'aut_label': '3O', 'centralizer': '72.CK', 'counter': 23, 'group_counter': 466, 'group_order': 944784, 'label': '3O', 'order': 3, 'powers': [23, 1], 'representative': 10628907027100423040501723775263215760884, 'size': 72}
    • id: 170339516
      {'aut_label': '3P', 'centralizer': '72.O', 'counter': 24, 'group_counter': 466, 'group_order': 944784, 'label': '3P', 'order': 3, 'powers': [24, 1], 'representative': 10631640229188454196371309587993202884624, 'size': 72}
    • id: 170339527
      {'aut_label': '3P', 'centralizer': '72.O', 'counter': 25, 'group_counter': 466, 'group_order': 944784, 'label': '3Q', 'order': 3, 'powers': [25, 1], 'representative': 10628907246882234597942383598288501966963, 'size': 72}
    • id: 170339538
      {'aut_label': '3P', 'centralizer': '72.O', 'counter': 26, 'group_counter': 466, 'group_order': 944784, 'label': '3R', 'order': 3, 'powers': [26, 1], 'representative': 20673086185888440953948351246609348250483, 'size': 72}
    • id: 170339549
      {'aut_label': '3P', 'centralizer': '72.O', 'counter': 27, 'group_counter': 466, 'group_order': 944784, 'label': '3S', 'order': 3, 'powers': [27, 1], 'representative': 127645583889940601142202240507586309606640, 'size': 72}
    • id: 170339560
      {'aut_label': '3P', 'centralizer': '72.O', 'counter': 28, 'group_counter': 466, 'group_order': 944784, 'label': '3T', 'order': 3, 'powers': [28, 1], 'representative': 20669555405071868659046346755787038340720, 'size': 72}
    • id: 170339571
      {'aut_label': '3P', 'centralizer': '72.O', 'counter': 29, 'group_counter': 466, 'group_order': 944784, 'label': '3U', 'order': 3, 'powers': [29, 1], 'representative': 20666567523914407690586276573163508882084, 'size': 72}
    • id: 170339583
      {'aut_label': '3P', 'centralizer': '72.O', 'counter': 30, 'group_counter': 466, 'group_order': 944784, 'label': '3V', 'order': 3, 'powers': [30, 1], 'representative': 6518881757426964224843000389033664640, 'size': 72}
    • id: 170339594
      {'aut_label': '3P', 'centralizer': '72.O', 'counter': 31, 'group_counter': 466, 'group_order': 944784, 'label': '3W', 'order': 3, 'powers': [31, 1], 'representative': 7045143430487768367790028984182442883, 'size': 72}
    • id: 170339605
      {'aut_label': '3P', 'centralizer': '72.O', 'counter': 32, 'group_counter': 466, 'group_order': 944784, 'label': '3X', 'order': 3, 'powers': [32, 1], 'representative': 526380712665423861557807245581966723, 'size': 72}
    • id: 170339616
      {'aut_label': '3Y', 'centralizer': '144.U', 'counter': 33, 'group_counter': 466, 'group_order': 944784, 'label': '3Y', 'order': 3, 'powers': [33, 1], 'representative': 418829647188114752493657747, 'size': 144}
    • id: 170339622
      {'aut_label': '3Z', 'centralizer': '144.J', 'counter': 34, 'group_counter': 466, 'group_order': 944784, 'label': '3Z', 'order': 3, 'powers': [34, 1], 'representative': 9151683496875285439911007224838, 'size': 144}
    • id: 170339623
      {'aut_label': '3Z', 'centralizer': '144.J', 'counter': 35, 'group_counter': 466, 'group_order': 944784, 'label': '3AA', 'order': 3, 'powers': [35, 1], 'representative': 9151683496880151243833955228114, 'size': 144}
    • id: 170339624
      {'aut_label': '3Z', 'centralizer': '144.J', 'counter': 36, 'group_counter': 466, 'group_order': 944784, 'label': '3AB', 'order': 3, 'powers': [36, 1], 'representative': 9156716574310145477197435087317, 'size': 144}
    • id: 170339625
      {'aut_label': '3Z', 'centralizer': '144.J', 'counter': 37, 'group_counter': 466, 'group_order': 944784, 'label': '3AC', 'order': 3, 'powers': [37, 1], 'representative': 9156716574312700024131663941634, 'size': 144}
    • id: 170339626
      {'aut_label': '3Z', 'centralizer': '144.J', 'counter': 38, 'group_counter': 466, 'group_order': 944784, 'label': '3AD', 'order': 3, 'powers': [38, 1], 'representative': 271362827271368330824930594632732118, 'size': 144}
    • id: 170339627
      {'aut_label': '3Z', 'centralizer': '144.J', 'counter': 39, 'group_counter': 466, 'group_order': 944784, 'label': '3AE', 'order': 3, 'powers': [39, 1], 'representative': 271362832304445767996224614471784914, 'size': 144}
    • id: 170339629
      {'aut_label': '3Z', 'centralizer': '144.J', 'counter': 40, 'group_counter': 466, 'group_order': 944784, 'label': '3AF', 'order': 3, 'powers': [40, 1], 'representative': 271463567735518196447053698568363443, 'size': 144}
    • id: 170339630
      {'aut_label': '3Z', 'centralizer': '144.J', 'counter': 41, 'group_counter': 466, 'group_order': 944784, 'label': '3AG', 'order': 3, 'powers': [41, 1], 'representative': 271463567735569900480908078775915683, 'size': 144}
    • id: 170339631
      {'aut_label': '3Z', 'centralizer': '144.J', 'counter': 42, 'group_counter': 466, 'group_order': 944784, 'label': '3AH', 'order': 3, 'powers': [42, 1], 'representative': 10628652136789894114949100773230730805814, 'size': 144}
    • id: 170339632
      {'aut_label': '3AI', 'centralizer': None, 'counter': 43, 'group_counter': 466, 'group_order': 944784, 'label': '3AI', 'order': 3, 'powers': [43, 1], 'representative': 20666822203592807611721071104246685869364, 'size': 324}
    • id: 170339633
      {'aut_label': '3AJ', 'centralizer': None, 'counter': 44, 'group_counter': 466, 'group_order': 944784, 'label': '3AJ', 'order': 3, 'powers': [44, 1], 'representative': 255293612331944736618355563005186875985520, 'size': 648}
    • id: 170339634
      {'aut_label': '3AJ', 'centralizer': None, 'counter': 45, 'group_counter': 466, 'group_order': 944784, 'label': '3AK', 'order': 3, 'powers': [45, 1], 'representative': 275960179627539264712221283161510017684643, 'size': 648}
    • id: 170339635
      {'aut_label': '3AJ', 'centralizer': None, 'counter': 46, 'group_counter': 466, 'group_order': 944784, 'label': '3AL', 'order': 3, 'powers': [46, 1], 'representative': 6519074066202122562030385109362017988, 'size': 648}
    • id: 170339636
      {'aut_label': '3AJ', 'centralizer': None, 'counter': 47, 'group_counter': 466, 'group_order': 944784, 'label': '3AM', 'order': 3, 'powers': [47, 1], 'representative': 275962879096746535237263778378146826137600, 'size': 648}
    • id: 170339637
      {'aut_label': '3AJ', 'centralizer': None, 'counter': 48, 'group_counter': 466, 'group_order': 944784, 'label': '3AN', 'order': 3, 'powers': [48, 1], 'representative': 10628652238143491040532133827105590796948, 'size': 648}
    • id: 170339638
      {'aut_label': '3AJ', 'centralizer': None, 'counter': 49, 'group_counter': 466, 'group_order': 944784, 'label': '3AO', 'order': 3, 'powers': [49, 1], 'representative': 20666567414032357383310647555734050448160, 'size': 648}
    • id: 170339640
      {'aut_label': '3AP', 'centralizer': None, 'counter': 50, 'group_counter': 466, 'group_order': 944784, 'label': '3AP', 'order': 3, 'powers': [50, 1], 'representative': 20672814832212853030786466686402375923844, 'size': 1296}
    • id: 170339641
      {'aut_label': '3AQ', 'centralizer': None, 'counter': 51, 'group_counter': 466, 'group_order': 944784, 'label': '3AQ', 'order': 3, 'powers': [51, 1], 'representative': 20670081841371405967934418258340728718323, 'size': 1296}
    • id: 170339642
      {'aut_label': '3AQ', 'centralizer': None, 'counter': 52, 'group_counter': 466, 'group_order': 944784, 'label': '3AR', 'order': 3, 'powers': [52, 1], 'representative': 6519000794999615422647984434884584960, 'size': 1296}
    • id: 170339643
      {'aut_label': '3AQ', 'centralizer': None, 'counter': 53, 'group_counter': 466, 'group_order': 944784, 'label': '3AS', 'order': 3, 'powers': [53, 1], 'representative': 526389258734795110315848848752204803, 'size': 1296}
    • id: 170339644
      {'aut_label': '3AQ', 'centralizer': None, 'counter': 54, 'group_counter': 466, 'group_order': 944784, 'label': '3AT', 'order': 3, 'powers': [54, 1], 'representative': 148314324411396952266962023600843800576147, 'size': 1296}
    • id: 170339645
      {'aut_label': '3AP', 'centralizer': None, 'counter': 55, 'group_counter': 466, 'group_order': 944784, 'label': '3AU', 'order': 3, 'powers': [55, 1], 'representative': 20666567286458362769418742099094233649878, 'size': 1296}
    • id: 170339646
      {'aut_label': '3AQ', 'centralizer': None, 'counter': 56, 'group_counter': 466, 'group_order': 944784, 'label': '3AV', 'order': 3, 'powers': [56, 1], 'representative': 10634899839492757775998552832091399009843, 'size': 1296}
    • id: 170339647
      {'aut_label': '3AP', 'centralizer': None, 'counter': 57, 'group_counter': 466, 'group_order': 944784, 'label': '3AW', 'order': 3, 'powers': [57, 1], 'representative': 265918733642754849836833286796540044282404, 'size': 1296}
    • id: 170339648
      {'aut_label': '3AQ', 'centralizer': None, 'counter': 58, 'group_counter': 466, 'group_order': 944784, 'label': '3AX', 'order': 3, 'powers': [58, 1], 'representative': 3785807854877150649117084435904354083, 'size': 1296}
    • id: 170339649
      {'aut_label': '4A', 'centralizer': None, 'counter': 59, 'group_counter': 466, 'group_order': 944784, 'label': '4A', 'order': 4, 'powers': [5, 59], 'representative': 31912533505267176923640603544283986832045, 'size': 13122}
    • id: 170339651
      {'aut_label': '4A', 'centralizer': None, 'counter': 60, 'group_counter': 466, 'group_order': 944784, 'label': '4B', 'order': 4, 'powers': [5, 60], 'representative': 169891002303715737716760530065079717989920, 'size': 13122}
    • id: 170339652
      {'aut_label': '6A', 'centralizer': '108.DD', 'counter': 61, 'group_counter': 466, 'group_order': 944784, 'label': '6A', 'order': 6, 'powers': [12, 2], 'representative': 4897391030895396492310643703906468212, 'size': 108}
    • id: 170339653
      {'aut_label': '6B', 'centralizer': '108.DD', 'counter': 62, 'group_counter': 466, 'group_order': 944784, 'label': '6B', 'order': 6, 'powers': [12, 2], 'representative': 63823470708729103409538985592640653394724, 'size': 108}
    • id: 170339654
      {'aut_label': '6C', 'centralizer': '108.A', 'counter': 63, 'group_counter': 466, 'group_order': 944784, 'label': '6C', 'order': 6, 'powers': [11, 2], 'representative': 63823725616727382925148646341997701238004, 'size': 108}
    • id: 170339655
      {'aut_label': '6D', 'centralizer': '108.DD', 'counter': 64, 'group_counter': 466, 'group_order': 944784, 'label': '6D', 'order': 6, 'powers': [9, 2], 'representative': 191468239887785581511602976676157066897204, 'size': 108}
    • id: 170339656
      {'aut_label': '6D', 'centralizer': '108.DD', 'counter': 65, 'group_counter': 466, 'group_order': 944784, 'label': '6E', 'order': 6, 'powers': [10, 2], 'representative': 319113008793365586070953950347930935902884, 'size': 108}
    • id: 170339657
      {'aut_label': '6F', 'centralizer': '216.A', 'counter': 66, 'group_counter': 466, 'group_order': 944784, 'label': '6F', 'order': 6, 'powers': [14, 2], 'representative': 1637973028623752769529704877046410196, 'size': 216}
    • id: 170339658
      {'aut_label': '6G', 'centralizer': '216.A', 'counter': 67, 'group_counter': 466, 'group_order': 944784, 'label': '6G', 'order': 6, 'powers': [15, 2], 'representative': 1637973029011533020612979607597680599, 'size': 216}
    • id: 170339659
      {'aut_label': '6G', 'centralizer': '216.A', 'counter': 68, 'group_counter': 466, 'group_order': 944784, 'label': '6H', 'order': 6, 'powers': [16, 2], 'representative': 1637973029430335691782916322570992595, 'size': 216}
    • id: 170339660
      {'aut_label': '6I', 'centralizer': '216.A', 'counter': 69, 'group_counter': 466, 'group_order': 944784, 'label': '6I', 'order': 6, 'powers': [17, 2], 'representative': 10630273654990332597922274055249945763895, 'size': 216}
    • id: 170339662
      {'aut_label': '6J', 'centralizer': None, 'counter': 70, 'group_counter': 466, 'group_order': 944784, 'label': '6J', 'order': 6, 'powers': [21, 2], 'representative': 1637963881973441394131691259228771796, 'size': 972}
    • id: 170339663
      {'aut_label': '6K', 'centralizer': None, 'counter': 71, 'group_counter': 466, 'group_order': 944784, 'label': '6K', 'order': 6, 'powers': [13, 3], 'representative': 233719353838118445477878711885262681985925, 'size': 972}
    • id: 170339664
      {'aut_label': '6L', 'centralizer': None, 'counter': 72, 'group_counter': 466, 'group_order': 944784, 'label': '6L', 'order': 6, 'powers': [9, 4], 'representative': 42244874745189297966050124371866686870213, 'size': 972}
    • id: 170339665
      {'aut_label': '6K', 'centralizer': None, 'counter': 73, 'group_counter': 466, 'group_order': 944784, 'label': '6M', 'order': 6, 'powers': [13, 4], 'representative': 244052238747240827437132494940092717495864, 'size': 972}
    • id: 170339666
      {'aut_label': '6L', 'centralizer': None, 'counter': 74, 'group_counter': 466, 'group_order': 944784, 'label': '6N', 'order': 6, 'powers': [10, 3], 'representative': 52577488429469468544506721725051209204319, 'size': 972}
    • id: 170339667
      {'aut_label': '6O', 'centralizer': None, 'counter': 75, 'group_counter': 466, 'group_order': 944784, 'label': '6O', 'order': 6, 'powers': [10, 5], 'representative': 74456188888926066717809910085754287646035, 'size': 1458}
    • id: 170339668
      {'aut_label': '6O', 'centralizer': None, 'counter': 76, 'group_counter': 466, 'group_order': 944784, 'label': '6P', 'order': 6, 'powers': [9, 5], 'representative': 84494104056272607558332975914793702942131, 'size': 1458}
    • id: 170339669
      {'aut_label': '6Q', 'centralizer': None, 'counter': 77, 'group_counter': 466, 'group_order': 944784, 'label': '6Q', 'order': 6, 'powers': [22, 2], 'representative': 202096620635527418787413053229832138340080, 'size': 1944}
    • id: 170339670
      {'aut_label': '6R', 'centralizer': None, 'counter': 78, 'group_counter': 466, 'group_order': 944784, 'label': '6R', 'order': 6, 'powers': [24, 2], 'representative': 329747908440547567715541154418835820661760, 'size': 1944}
    • id: 170339671
      {'aut_label': '6R', 'centralizer': None, 'counter': 79, 'group_counter': 466, 'group_order': 944784, 'label': '6S', 'order': 6, 'powers': [25, 2], 'representative': 20674979140190290650305000166394446162932, 'size': 1944}
    • id: 170339673
      {'aut_label': '6R', 'centralizer': None, 'counter': 80, 'group_counter': 466, 'group_order': 944784, 'label': '6T', 'order': 6, 'powers': [26, 2], 'representative': 191471499306391338360303054046158182878084, 'size': 1944}
    • id: 170339674
      {'aut_label': '6R', 'centralizer': None, 'counter': 81, 'group_counter': 466, 'group_order': 944784, 'label': '6U', 'order': 6, 'powers': [27, 2], 'representative': 275961546218814132723719783062795846905479, 'size': 1944}
    • id: 170339675
      {'aut_label': '6R', 'centralizer': None, 'counter': 82, 'group_counter': 466, 'group_order': 944784, 'label': '6V', 'order': 6, 'powers': [28, 2], 'representative': 319119527665975168358379502845768746588400, 'size': 1944}
    • id: 170339676
      {'aut_label': '6W', 'centralizer': None, 'counter': 83, 'group_counter': 466, 'group_order': 944784, 'label': '6W', 'order': 6, 'powers': [18, 3], 'representative': 287204261288268383796312342692971167432719, 'size': 1944}
    • id: 170339677
      {'aut_label': '6R', 'centralizer': None, 'counter': 84, 'group_counter': 466, 'group_order': 944784, 'label': '6X', 'order': 6, 'powers': [29, 2], 'representative': 10633533183492851505566954453483505127826, 'size': 1944}
    • id: 170339678
      {'aut_label': '6R', 'centralizer': None, 'counter': 85, 'group_counter': 466, 'group_order': 944784, 'label': '6Y', 'order': 6, 'powers': [30, 2], 'representative': 202099608726677985403513227858035005837680, 'size': 1944}
    • id: 170339679
      {'aut_label': '6R', 'centralizer': None, 'counter': 86, 'group_counter': 466, 'group_order': 944784, 'label': '6Z', 'order': 6, 'powers': [31, 2], 'representative': 63825915279085584300498923143485989102788, 'size': 1944}
    • id: 170339680
      {'aut_label': '6W', 'centralizer': None, 'counter': 87, 'group_counter': 466, 'group_order': 944784, 'label': '6AA', 'order': 6, 'powers': [19, 4], 'representative': 32206433417527131931851106271651282457334, 'size': 1944}
    • id: 170339681
      {'aut_label': '6R', 'centralizer': None, 'counter': 88, 'group_counter': 466, 'group_order': 944784, 'label': '6AB', 'order': 6, 'powers': [32, 2], 'representative': 5152491339144433610182872678001508996, 'size': 1944}
    • id: 170339682
      {'aut_label': '6AC', 'centralizer': None, 'counter': 89, 'group_counter': 466, 'group_order': 944784, 'label': '6AC', 'order': 6, 'powers': [11, 6], 'representative': 201803272384479011935996482969413301014877, 'size': 2916}
    • id: 170339684
      {'aut_label': '6AD', 'centralizer': None, 'counter': 90, 'group_counter': 466, 'group_order': 944784, 'label': '6AD', 'order': 6, 'powers': [13, 6], 'representative': 74157162196213028447718883100237742543388, 'size': 2916}
    • id: 170339685
      {'aut_label': '6AE', 'centralizer': None, 'counter': 91, 'group_counter': 466, 'group_order': 944784, 'label': '6AE', 'order': 6, 'powers': [12, 5], 'representative': 339784457033702247311422301222911786202885, 'size': 2916}
    • id: 170339686
      {'aut_label': '6AF', 'centralizer': None, 'counter': 92, 'group_counter': 466, 'group_order': 944784, 'label': '6AF', 'order': 6, 'powers': [11, 7], 'representative': 191769439742836504492243482352291923371371, 'size': 8748}
    • id: 170339687
      {'aut_label': '6AG', 'centralizer': None, 'counter': 93, 'group_counter': 466, 'group_order': 944784, 'label': '6AG', 'order': 6, 'powers': [43, 4], 'representative': 42244874947296393554313116359778753349570, 'size': 8748}
    • id: 170339688
      {'aut_label': '6AH', 'centralizer': None, 'counter': 94, 'group_counter': 466, 'group_order': 944784, 'label': '6AH', 'order': 6, 'powers': [21, 7], 'representative': 212430031668321041008701097094846426065771, 'size': 8748}
    • id: 170339689
      {'aut_label': '6AG', 'centralizer': None, 'counter': 95, 'group_counter': 466, 'group_order': 944784, 'label': '6AI', 'order': 6, 'powers': [43, 3], 'representative': 223680912409098456079942498646779555628165, 'size': 8748}
    • id: 170339690
      {'aut_label': '6AJ', 'centralizer': None, 'counter': 96, 'group_counter': 466, 'group_order': 944784, 'label': '6AJ', 'order': 6, 'powers': [44, 4], 'representative': 169889372599302186886050322141293760466518, 'size': 17496}
    • id: 170339691
      {'aut_label': '6AJ', 'centralizer': None, 'counter': 97, 'group_counter': 466, 'group_order': 944784, 'label': '6AK', 'order': 6, 'powers': [45, 4], 'representative': 297537146105833748849201211472549615059573, 'size': 17496}
    • id: 170339692
      {'aut_label': '6AJ', 'centralizer': None, 'counter': 98, 'group_counter': 466, 'group_order': 944784, 'label': '6AL', 'order': 6, 'powers': [46, 3], 'representative': 106068880890487124350807616442198676333682, 'size': 17496}
    • id: 170339693
      {'aut_label': '6AM', 'centralizer': None, 'counter': 99, 'group_counter': 466, 'group_order': 944784, 'label': '6AM', 'order': 6, 'powers': [23, 7], 'representative': 276254037612162635476035996504613249989693, 'size': 17496}
    • id: 170339362
      {'aut_label': '6AJ', 'centralizer': None, 'counter': 100, 'group_counter': 466, 'group_order': 944784, 'label': '6AN', 'order': 6, 'powers': [47, 3], 'representative': 159559492291733201058143379185762648270015, 'size': 17496}
  • group 944784.rx does not appear in gps_qchar
  • group 944784.rx does not appear in gps_char
  • gps_subgroup_search • Show schema
    Showing the first 100 of 878 matching records in this table.
    • id: 259934712
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 944784, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '944784.rx.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': '944784.rx', 'subgroup_hash': 4214627173336113295, 'subgroup_order': 944784, 'subgroup_tex': 'C_3^6.S_3^2:S_3^2', 'supersolvable': False, 'sylow': 0}
    • id: 259934823
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 472392, 'counter': 2, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.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': '472392.rw', 'subgroup_hash': 4458908981959553522, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3\\wr D_4', 'supersolvable': False, 'sylow': 0}
    • id: 259934934
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 472392, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6905203737013556544, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935045
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 472392, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.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': '472392.sn', 'subgroup_hash': 1440794149021317160, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^3:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 259935156
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 472392, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.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': '472392.sf', 'subgroup_hash': 5139320985986329917, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3:S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935267
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 472392, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.2.E', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '472392.sq', 'subgroup_hash': 3652164612811462139, 'subgroup_order': 472392, 'subgroup_tex': 'C_3^6.C_3^3:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 259935378
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 157464, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '314928.pl', 'subgroup_hash': 2343006311215618144, 'subgroup_order': 314928, 'subgroup_tex': 'C_3^4:D_9^2.D_6', 'supersolvable': False, 'sylow': 0}
    • id: 259935489
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 236196, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.4.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 340208659364747194, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^5.C_3^3.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935579
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.4.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.lh', 'subgroup_hash': 8198807337538431408, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259934713
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 236196, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.4.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1774167739767186062, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259934724
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 236196, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.4.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 785818130423123813, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259934735
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 236196, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.4.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.lt', 'subgroup_hash': 8205912189180883211, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3\\wr C_4', 'supersolvable': False, 'sylow': 0}
    • id: 259934746
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.4.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8798678059431488685, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^5.C_3^4.C_6.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259934757
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.4.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5646878397580738634, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259934768
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.4.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '236196.lh', 'subgroup_hash': 8198807337538431408, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259934779
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 118098, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.4.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7450749825844581627, 'subgroup_order': 236196, 'subgroup_tex': 'C_3^6.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259934790
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 157464, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.qx', 'subgroup_hash': 1425006708033936817, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.S_3^2:S_3', 'supersolvable': False, 'sylow': 0}
    • id: 259934801
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1941662713246547236, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^5.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 259934812
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.sb', 'subgroup_hash': 889702245471581537, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^4:D_9^2.C_6', 'supersolvable': False, 'sylow': 0}
    • id: 259934824
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2433278420634585874, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^5.C_3.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 259934835
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4169309858383769646, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 259934846
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.rt', 'subgroup_hash': 7761177235173255138, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^4:D_9^2.S_3', 'supersolvable': False, 'sylow': 0}
    • id: 259934857
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.rl', 'subgroup_hash': 2993312798010071895, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^4.C_3^4:D_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 259934868
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.rd', 'subgroup_hash': 8424162991384224056, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 259934879
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.rd', 'subgroup_hash': 8424162991384224056, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^6.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 259934890
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.6.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '157464.ro', 'subgroup_hash': 2952802470595129241, 'subgroup_order': 157464, 'subgroup_tex': 'C_3^4.C_3^4:(C_4\\times S_3)', 'supersolvable': False, 'sylow': 0}
    • id: 259934901
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 118098, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.8.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3518229174562669243, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259934912
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 118098, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.8.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3518229174562669243, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^5.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 259934923
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 118098, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.8.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1829385611185224045, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259934935
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.8.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7894505538339019415, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259934946
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.8.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4514826845252250347, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259934957
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 59049, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.8.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 38104853317048767, 'subgroup_order': 118098, 'subgroup_tex': 'C_3^6.C_3^4.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259934968
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.9.A', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '104976.nt', 'subgroup_hash': 812285917969530294, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^4.D_{18}:D_{18}', 'supersolvable': False, 'sylow': 0}
    • id: 259934979
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.9.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5861407378612664923, 'subgroup_order': 104976, 'subgroup_tex': 'C_3^6.C_3:S_3.C_2^3', 'supersolvable': False, 'sylow': 0}
    • id: 259934990
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4110140613294239226, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^3.C_6.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935001
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6539010332495766906, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.\\He_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935012
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 78732, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.ld', 'subgroup_hash': 7060085343048531467, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3:C_4', 'supersolvable': False, 'sylow': 0}
    • id: 259935023
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5389091165748985415, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935034
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6152936847367844926, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^2.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935046
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3038864083403252876, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935057
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2887769734126036847, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^3.C_3^5.C_6.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935068
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3492160101948426685, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935079
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8040346015523948974, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^2.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935090
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5707762305548386369, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^2.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935101
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8109013156988072544, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935112
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6516675936263672912, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^4.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935123
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6516675936263672912, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^4.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935134
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4465805208545800867, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^4.C_3^5.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935145
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7403022519798561526, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^2.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935157
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7403022519798561526, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.\\He_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935168
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.Q', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5347452293411049836, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^2.C_6^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935179
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2228602622603136301, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^3.C_6.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935190
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.S', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8906847388816749675, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935201
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.T', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8906847388816749675, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935212
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.U', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6713378673419489337, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935223
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.V', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6713378673419489337, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^3.C_2^2', 'supersolvable': True, 'sylow': 0}
    • id: 259935234
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.W', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7254989324136141937, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^2.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935245
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.X', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4288560468425506091, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.\\He_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935256
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.Y', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4288560468425506091, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.\\He_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935268
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.Z', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6539010332495766906, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^2.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935279
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.BA', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1269779721976825000, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935290
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.BB', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1124187335215783779, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.\\He_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935301
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.BC', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9110624096294355116, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935312
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.BD', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1269779721976825000, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935323
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.BE', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1124187335215783779, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^6.C_3^2.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935334
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.BF', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 657359263054080783, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.C_3^3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935345
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8133261132594982920, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^5.\\He_3.D_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935356
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.12.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '78732.li', 'subgroup_hash': 4094729405608444377, 'subgroup_order': 78732, 'subgroup_tex': 'C_3^4.C_3^4:C_{12}', 'supersolvable': False, 'sylow': 0}
    • id: 259935367
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 59049, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '944784.rx.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['F', 'L2', 'C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 56042109095087524, 'subgroup_order': 59049, 'subgroup_tex': 'C_3^6.C_3^4', 'supersolvable': True, 'sylow': 3}
    • id: 259935379
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.oz', 'subgroup_hash': 3894498303307350474, 'subgroup_order': 52488, 'subgroup_tex': '(C_3:S_3:C_9)\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 259935390
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6060167105608968810, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.C_3.D_6.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935401
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8105160746397636669, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935412
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 524607090200736018, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935423
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5255810189357614959, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935434
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3258585948616446184, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.C_3.D_6.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935445
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6599697163612110075, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935456
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 9063690763117432479, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.S_3\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 259935467
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 26244, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 3336341356835834475, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935478
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.nq', 'subgroup_hash': 5661099390323521140, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.C_3:D_{36}', 'supersolvable': False, 'sylow': 0}
    • id: 259935490
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 2688935282076775699, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^6.S_3\\wr C_2', 'supersolvable': False, 'sylow': 0}
    • id: 259935501
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8092114055544823793, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935512
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 8092114055544823793, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3^4.C_2^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935523
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1400815484695369191, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^5.S_3^3', 'supersolvable': True, 'sylow': 0}
    • id: 259935534
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '52488.nx', 'subgroup_hash': 7698216172695423692, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4:C_{18}.D_{18}', 'supersolvable': False, 'sylow': 0}
    • id: 259935545
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13122, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.18.P', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 6939542149107927342, 'subgroup_order': 52488, 'subgroup_tex': 'C_3^4.C_3^4.C_2^2.C_2', 'supersolvable': False, 'sylow': 0}
    • id: 259935556
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 39366, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1', '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': 1617664516712860841, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935567
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7538404885108620235, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935577
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.C', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 567972047900213034, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^3.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935578
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1685517233765596824, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935580
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.E', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5396640384538962852, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^4.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935581
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.F', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5396640384538962852, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^4.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935582
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 1206738856853824893, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^4.C_3^5.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935583
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 729, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.H', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4335326722565386717, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^3.C_3^4.C_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935584
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.I', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4335326722565386717, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^4.C_3^4.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935585
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7999269442015727279, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935586
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.K', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4144341226551984197, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935587
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4144341226551984197, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^5.\\He_3.C_6', 'supersolvable': True, 'sylow': 0}
    • id: 259935588
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2187, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 5955212944316845953, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259935589
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 6561, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.N', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7877293562513805723, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
    • id: 259934714
      {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '944784.rx', 'ambient_counter': 466, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.S_3^2:S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 19683, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.rx.24.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 7877293562513805723, 'subgroup_order': 39366, 'subgroup_tex': 'C_3^6.C_3^3.C_2', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    Showing the first 100 of 878 matching records in this table.
    • id: 259934712
      {'ambient': '944784.rx', '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': [24, 1642, 6, 179], 'generators': [244050880369023955532401898366136741200668, 17684330570401657831907612774644, 5152509022668445817602081497702731396, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 127651814341427291341507040516023521515254, 418802671169936714973312003, 3259463770706534265128308294164584130, 202098242143948411094716526875379787657842, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.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': '944784.rx', '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': '944784.rx'}
    • id: 259934713
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '4.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.C', 'coset_action_label': None, 'count': 1, 'diagramx': [358, 8447, 200, 3841], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 127651814341427291341507040516023521515254, 418802671169936714973312003, 3259463770706534265128308294164584130, 202098242143948411094716526875379787657842, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.4.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '944784.rx', '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': '944784.rx'}
    • id: 259934714
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 4, 'diagramx': [1234, -1, 1422, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 127584479652529225029754187324304, 418802671169936714973312003, 3259463770706534265128308294164584130, 26978572725239511210388, 351323236716841457582981799391071604180532, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '24.o1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.O', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934715
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 6, 'diagramx': [428, -1, 1182, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 3259463770706534265128308294164584130, 202098242143948411094716526875379787657842, 5839768424695184672943013074, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.p1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.P', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934716
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 6, 'diagramx': [67, -1, 1075, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 275962352962651695408739719452801998844164, 418802671169936714973312003, 202098242143948411094716526875379787657842, 275959908356282400148388405536365721106068, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.q1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Q', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934717
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 2, 'diagramx': [998, -1, 1351, -1], 'generators': [202098242143948411094716526875379787657842, 5839768424695184672943013074, 127651814341427291341507040516023521515254, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 3259463770706534265128308294164584130, 418802671169936714973312003], 'label': '944784.rx.24.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '24.r1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.R', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934718
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.B', 'coset_action_label': None, 'count': 6, 'diagramx': [468, -1, 1194, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 201803017568052333615023641991654524717707, 3259463770706534265128308294164584130, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.D', 'old_label': '24.s1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.S', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934719
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [23, -1, 1061, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 201803017568052333615023641991654524717707, 237475337926402312641649968687507, 3259463770706534265128308294164584130, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.t1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.T', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934720
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.U', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.B', 'coset_action_label': None, 'count': 2, 'diagramx': [957, -1, 1340, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 3259463770706534265128308294164584130, 5839768424695184672943013074, 275959908429557765295566733700529155577014, 26978572725239511210388, 74160421623357756629837947595896246623624, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '24.u1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.U', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934721
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.V', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.B', 'coset_action_label': None, 'count': 2, 'diagramx': [147, -1, 1098, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 275962352962651695408739719452801998844164, 418802671169936714973312003, 275959908356282400148388405536365721106068, 275959908429557765295566733700529155577014, 26978572725239511210388, 74160421623357756629837947595896246623624, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '24.v1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.V', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934722
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1116, -1, 1387, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 300393531205830864744611142798001520394, 3259463770706534265128308294164584130, 127651814341429807909604074251360238547908, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.J', 'old_label': '24.w1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.W', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934723
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [300393531205830864744611142798001520394, 5839768424695184672943013074, 127651814341427291341507040516023521515254, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 3259463770706534265128308294164584130, 418802671169936714973312003], 'label': '944784.rx.24.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.D', 'old_label': '24.xB', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.X', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934724
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '4.D', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.D', 'coset_action_label': None, 'count': 1, 'diagramx': [279, 6806, 176, 3511], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 127651814341427291341507040516023521515254, 418802671169936714973312003, 300393531205830864744611142798001520394, 3259463770706534265128308294164584130, 202098242143948411094716526875379787657842, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.4.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '944784.rx', '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': '944784.rx'}
    • id: 259934725
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.B', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [300393531205830864744611142798001520394, 127651814341427291341507040516023521515254, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 127575671634220312183477031038323, 3259463770706534265128308294164584130, 418802671169936714973312003], 'label': '944784.rx.24.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.D', 'old_label': '24.xC', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Y', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934726
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1077, -1, 1375, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 300393531205830864744611142798001520394, 3259463770706534265128308294164584130, 5839768424695184672943013074, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.y1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.Z', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934727
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [625, -1, 1241, -1], 'generators': [300393531205830864744611142798001520394, 5839768424695184672943013074, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 3259463770706534265128308294164584130, 418802671169936714973312003, 127584479652529225029754187324304], 'label': '944784.rx.24.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.z1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BA', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934728
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1408, -1, 1474, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 418802671169936714973312003, 300393531205830864744611142798001520394, 3259463770706534265128308294164584130, 275959908356282400148388405536365721106068, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.ba1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BB', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934729
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1369, -1, 1462, -1], 'generators': [300393531205830864744611142798001520394, 127651814341427291341507040516023521515254, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 3259463770706534265128308294164584130, 418802671169936714973312003, 127584479652529225029754187324304], 'label': '944784.rx.24.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '24.bb1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934730
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 2, 'diagramx': [1536, -1, 1512, -1], 'generators': [276253511368172292103428529232088284191290, 127645855444463450935263691676363382286080, 17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 127651814341429807909604074251360238547908, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '24.bc1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934731
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 24, 'diagramx': [383, -1, 1169, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 275962352962651695408739719452801998844164, 418802671169936714973312003, 127651814341429807909604074251360238547908, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.BE', 'old_label': '24.bd1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934732
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 24, 'diagramx': [335, -1, 1154, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 418802671169936714973312003, 3259463770706534265128308294164584130, 127651814341429807909604074251360238547908, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.J', 'old_label': '24.be1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934733
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 24, 'diagramx': [1492, -1, 1499, -1], 'generators': [5839768424695184672943013074, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 295241022183162551778698202493878165145, 10628907036246685625578073782240332522387, 4865804190709907763, 418802671169936714973312003, 127584479652529225029754187324304, 275962352962651695408739719452801998844164], 'label': '944784.rx.24.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.W', 'old_label': '24.bf1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BG', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934734
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.B', 'coset_action_label': None, 'count': 6, 'diagramx': [546, -1, 1217, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 3259463770706534265128308294164584130, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.D', 'old_label': '24.bg1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BH', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934735
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '4.E', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '4.E', 'coset_action_label': None, 'count': 2, 'diagramx': [109, 3324, 126, 2810], 'generators': [17684330570401657831907612774644, 244346104944920001937955052654412440330385, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 127651814341427291341507040516023521515254, 418802671169936714973312003, 3259463770706534265128308294164584130, 202098242143948411094716526875379787657842, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.4.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '944784.rx', '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': None}
    • id: 259934736
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 6, 'diagramx': [586, -1, 1229, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 3259463770706534265128308294164584130, 5839768424695184672943013074, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '24.bh1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BI', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934737
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1448, -1, 1486, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 418802671169936714973312003, 3259463770706534265128308294164584130, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '24.bi1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BJ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934738
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 12, 'diagramx': [287, -1, 1140, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 418802671169936714973312003, 3259463770706534265128308294164584130, 275959908356282400148388405536365721106068, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.O', 'old_label': '24.bj1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BK', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934739
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 6, 'diagramx': [239, -1, 1126, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 275962352962651695408739719452801998844164, 418802671169936714973312003, 275959908356282400148388405536365721106068, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.bk1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BL', 'subgroup_fusion': None, 'weyl_group': '157464.rd'}
    • id: 259934740
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '24.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '48.A', 'coset_action_label': None, 'count': 6, 'diagramx': [191, -1, 1111, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 3259463770706534265128308294164584130, 237475337926402312641649968687507, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.24.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.bl1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.BM', 'subgroup_fusion': None, 'weyl_group': '314928.pl'}
    • id: 259934741
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 54, 'diagramx': [17, -1, 1523, -1], 'generators': [127648028551255131622442324925018588986404, 17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 351029896963370416307039779027355634051868, 74452658108100750333064508613122550948481, 418802671169936714973312003, 127649921414599317434560331203840986173492, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.27.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934742
      {'ambient': '944784.rx', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '36.A', 'coset_action_label': None, 'count': 1, 'diagramx': [2052, 1423, 2139, 7135], 'generators': [5423661851800953859178358486848134772, 17684330570401657831907612774644, 191472051032343538037001321677135365749125, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 3259463770706534265128308294164584130, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '944784.rx', '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': None}
    • id: 259934743
      {'ambient': '944784.rx', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1534, -1, 1985, -1], 'generators': [74160421623357756629837947595896246623624, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 5152509022668445817602081497702731396, 275956920273669094988638454985559303454644, 418802671169936714973312003, 148318110282738971469764531982920863334643, 265921993271357068235195980682261266325494, 127645855444463450959994261899895606199748], 'label': '944784.rx.36.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '36.b1', 'projective_image': '944784.rx', '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': None}
    • id: 259934744
      {'ambient': '944784.rx', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2351, -1, 2228, -1], 'generators': [17684330570401657831907612774644, 275958286791666469200145785571593592407092, 295241022183162551778698202493878165145, 271353676394454377792702129150099764, 127645855444463450959994261899895606199748, 148317584021065104082709063350993847885040, 275956920273669094988638454985559303454644, 418802671169936714973312003, 275959908429557765295566733700529155577014, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '36.c1', 'projective_image': '944784.rx', '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': None}
    • id: 259934745
      {'ambient': '944784.rx', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2576, -1, 2295, -1], 'generators': [17684330570401657831907612774644, 271353676394454377792702129150099764, 275959908356289079275440747840674972603584, 275962352962651695408739719452801998844164, 418802671169936714973312003, 127651814341427291341504485969089292660930, 201803017568052333615023641991654524717707, 4897601024807732876556721653637451395, 127575671634220312183477031038323, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.D', 'old_label': '36.d1', 'projective_image': '944784.rx', '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': None}
    • id: 259934746
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '4.F', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '8.B', 'coset_action_label': None, 'count': 2, 'diagramx': [153, -1, 139, -1], 'generators': [17684330570401657831907612774644, 5152509022668445817602081497702731396, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 127651814341427291341507040516023521515254, 418802671169936714973312003, 201803017568052333615023641991654524717707, 3259463770706534265128308294164584130, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.4.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '4.f1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.F', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934747
      {'ambient': '944784.rx', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3041, -1, 2433, -1], 'generators': [74160421623357756629837947595896246623624, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 5152509022668445817602081497702731396, 4865804190709907763, 127575671634220312183477031038323, 418802671169936714973312003, 127645855444463450935263691676363382286080], 'label': '944784.rx.36.E', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '36.e1', 'projective_image': '944784.rx', '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': None}
    • id: 259934748
      {'ambient': '944784.rx', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [871, -1, 1788, -1], 'generators': [127645855444463450935263691676363382286080, 17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 1637963889910918891380036126878157955, 418802671169936714973312003, 127651814341429807909604074251360238547908, 26978572725239511210388, 74160421623357756629837947595896246623624, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '36.f1', 'projective_image': '944784.rx', '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': None}
    • id: 259934749
      {'ambient': '944784.rx', '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': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2395, -1, 2241, -1], 'generators': [2164427020010358586814490815719916131, 275959908282403518690324474174807783429810, 74160421623357756629837947595896246623624, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 418802671169936714973312003, 127645855444463450935263691676363382286080], 'label': '944784.rx.36.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '36.g1', 'projective_image': '944784.rx', '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: 259934750
      {'ambient': '944784.rx', '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': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.B', 'coset_action_label': None, 'count': 6, 'diagramx': [3120, -1, 2457, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 127653180850277563395451136404310139427799, 7045161123238576809862975502817589074, 418802671169936714973312003, 275959908429557765295566733700529155577014, 26978572725239511210388, 74160421623357756629837947595896246623624, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '36.h1', 'projective_image': '944784.rx', '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': None}
    • id: 259934751
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [208, -1, 1590, -1], 'generators': [3259463770706482556228691568819768918, 127651814341427291341507040516023521515254, 271353676394454377792702129150099764, 17684330570401657831907612774644, 295241022183162551778698202493878165145, 10628907036246685625578073782240332522387, 5152509022668445817602081497702731396, 127575671634220312183477031038323, 418802671169936714973312003, 7045161119044941337086923963671391730], 'label': '944784.rx.36.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.D', 'old_label': '36.i1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.I', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934752
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2097, -1, 2152, -1], 'generators': [17684330570401657831907612774644, 275958286791666469200145785571593592407092, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127648028478627178971074168090387840225157, 7045161123238576809862975502817589074, 418802671169936714973312003, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.J', 'old_label': '36.j1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.J', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934753
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 72, 'diagramx': [827, -1, 1774, -1], 'generators': [17684330570401657831907612774644, 275958286791666469200145785571593592407092, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 3259546183945186061262378455052098164, 127651814341429807909604074251360238547908, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.K', 'old_label': '36.k1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.K', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934754
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [3001, -1, 2422, -1], 'generators': [127645855444463450935263691676363382286080, 17684330570401657831907612774644, 275958286791666469200145785571593592407092, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 26978572725239511210388, 10628907036246685625578073782240332522387, 127575671634220312183477031038323], 'label': '944784.rx.36.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '36.l1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.L', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934755
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.M', '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': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [329, -1, 1626, -1], 'generators': [127645855444463450935263691676363382286080, 17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127650192850692758257313700359384128160516, 418802671169936714973312003, 127651814341429807909604074251360238547908, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '36.m1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.M', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934756
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.N', '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': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1152, -1, 1871, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127648028478627178971074168090387840225157, 418802671169936714973312003, 127647748178979357422541936656559771434405, 127651814341429807909604074251360238547908, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.N', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.N', 'old_label': '36.n1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.N', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934757
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '4.G', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '8.C', 'coset_action_label': None, 'count': 2, 'diagramx': [239, -1, 164, -1], 'generators': [17684330570401657831907612774644, 5152509022668445817602081497702731396, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 127651814341427291341507040516023521515254, 418802671169936714973312003, 3259463770706534265128308294164584130, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.4.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.B', 'old_label': '4.g1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.G', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934758
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.O', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 18, 'diagramx': [374, -1, 1640, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 7045161123238576809862975502817589074, 418802671169936714973312003, 127647748178979357422541936656559771434405, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '36.o1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.O', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934759
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.P', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1115, -1, 1860, -1], 'generators': [127645855444463450935263691676363382286080, 17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 275959908282403518690324474174807783429810, 418802671169936714973312003, 127649921414599317434560331203840986173492, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.P', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '36.p1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.P', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934760
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.Q', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 9, 'diagramx': [2887, -1, 2388, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 127653180850277563395451136404310139427799, 7045161123238576809862975502817589074, 418802671169936714973312003, 202098242143948411094716526875379787657842, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.Q', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '36.q1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.Q', 'subgroup_fusion': None, 'weyl_group': '74112.j'}
    • id: 259934761
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.R', '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': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2009, -1, 2126, -1], 'generators': [8156827311756021545929683248159711879, 3259463770706482556228691568819768918, 127651814341427291341507040516023521515254, 271353676394454377792702129150099764, 17684330570401657831907612774644, 201803017568052333615023641991654524717707, 10628907036246685625578073782240332522387, 4865804190709907763, 3259463762317318627384352499074778384, 418802671169936714973312003], 'label': '944784.rx.36.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.D', 'old_label': '36.r1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.R', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934762
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.S', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 36, 'diagramx': [786, -1, 1762, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 3259463770706482556228691568819768918, 127651814341427291341507040516023521515254, 1637963889910918891380036126878157955, 7045161123238576809862975502817589074, 418802671169936714973312003, 201803017568052333615023641991654524717707, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.S', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.S', 'old_label': '36.s1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.S', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934763
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.T', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.B', 'coset_action_label': None, 'count': 18, 'diagramx': [1841, -1, 2076, -1], 'generators': [5423661851800953859178358486848134772, 17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 201803017568052333615023641991654524717707, 3259463770706534265128308294164584130, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.T', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.I', 'old_label': '36.t1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.T', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934764
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.U', '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': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2809, -1, 2364, -1], 'generators': [127653180850277563395451136404310139427799, 3259463770706482556228691568819768918, 74160421623357756629837947595896246623624, 271353676394454377792702129150099764, 5451961195039184958188511090, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 418802671169936714973312003, 275959908447240901527518204918667984917730], 'label': '944784.rx.36.U', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '36.u1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.U', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934765
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.V', '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': '11664.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2851, -1, 2377, -1], 'generators': [127653180850277563395451136404310139427799, 5839768424695184672943013074, 3259463770706482556228691568819768918, 74160421623357756629837947595896246623624, 271353676394454377792702129150099764, 17684330570401657831907612774644, 275959908429557765295566733700529155577014, 10628907036246685625578073782240332522387, 4865804190709907763, 418802671169936714973312003], 'label': '944784.rx.36.V', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.V', 'old_label': '36.v1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.V', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934766
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.W', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2486, -1, 2268, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 1637963889910918891380036126878157955, 418802671169936714973312003, 3259463770706534265128308294164584130, 5839768424695184672943013074, 26978572725239511210388, 74160421623357756629837947595896246623624, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.W', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.D', 'old_label': '36.w1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.W', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934767
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.X', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1887, -1, 2090, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 127653180850277563395451136404310139427799, 275959908429559475276092744274398245060484, 418802671169936714973312003, 3259463770706534265128308294164584130, 26978572725239511210388, 74160421623357756629837947595896246623624, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.X', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.D', 'old_label': '36.x1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.X', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934768
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '4.H', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '8.B', 'coset_action_label': None, 'count': 2, 'diagramx': [67, -1, 113, -1], 'generators': [127651814341427291341507040516023521515254, 271353676394454377792702129150099764, 127584479652529225029754187324304, 26978572725239511210388, 5839768424695184672943013074, 201803017568052333615023641991654524717707, 17684330570401657831907612774644, 418802671169936714973312003, 3259463770706534265128308294164584130, 10628907036246685625578073782240332522387, 4865804190709907763, 244049793984571441653890772022859036635918], 'label': '944784.rx.4.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '4.h1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.H', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934769
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.Y', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2219, -1, 2189, -1], 'generators': [17684330570401657831907612774644, 127651814267542149426279400794859092356547, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 127649921414599317434560331203840986173492, 3259463770706534265128308294164584130, 26978572725239511210388, 74160421623357756629837947595896246623624, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.Y', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.E', 'old_label': '36.y1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.Y', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934770
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.Z', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2711, -1, 2335, -1], 'generators': [17684330570401657831907612774644, 5152509022668445817602081497702731396, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 3259463770706534265128308294164584130, 26978572725239511210388, 127575671634220312183477031038323, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.Z', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.Z', 'old_label': '36.z1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.Z', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934771
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2530, -1, 2281, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 1637963889910918891380036126878157955, 418802671169936714973312003, 3259463770706534265128308294164584130, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.E', 'old_label': '36.ba1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BA', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934772
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 72, 'diagramx': [1962, -1, 2112, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 3259463770706534265128308294164584130, 237475337926402312641649968687507, 2164427020010358586814490815719916131, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BB', 'old_label': '36.bb1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BB', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934773
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 18, 'diagramx': [2667, -1, 2322, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127653180850277563395451136404310139427799, 275959908429559475276092744274398245060484, 418802671169936714973312003, 3259463770706534265128308294164584130, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.F', 'old_label': '36.bc1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934774
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2263, -1, 2202, -1], 'generators': [17684330570401657831907612774644, 127651814267542149426279400794859092356547, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 127649921414599317434560331203840986173492, 3259463770706534265128308294164584130, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.G', 'old_label': '36.bd1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934775
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [2308, -1, 2216, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127650192850692758257313700359384128160516, 418802671169936714973312003, 3259463770706534265128308294164584130, 275959908356282400148388405536365721106068, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BE', 'old_label': '36.be1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934776
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.B', 'coset_action_label': None, 'count': 18, 'diagramx': [2622, -1, 2309, -1], 'generators': [5423661851800953859178358486848134772, 17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 3259463770706534265128308294164584130, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.I', 'old_label': '36.bf1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934777
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 9, 'contained_in': None, 'contains': None, 'core': '944784.a1', 'coset_action_label': '36T36457', 'count': 324, 'diagramx': [2441, -1, 2255, -1], 'generators': [17684330570401657831907612774644, 5152509022668445817602081497702731396, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127584479652529225029754187324304, 418802671169936714973312003, 3259463770706534265128308294164584130, 5839768424695184672943013074, 26978572725239511210388], 'label': '944784.rx.36.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BG', 'old_label': '36.bg1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BG', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934778
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3158, -1, 2468, -1], 'generators': [8156827311756021545929683248159711879, 3259463770706482556228691568819768918, 127651814341427291341507040516023521515254, 271353676394454377792702129150099764, 17684330570401657831907612774644, 298500485344092212256993321837624199679, 10628907036246685625578073782240332522387, 4865804190709907763, 3259463762317318627384352499074778384, 418802671169936714973312003], 'label': '944784.rx.36.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.D', 'old_label': '36.bh1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BH', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934779
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '4.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '8.C', 'coset_action_label': None, 'count': 2, 'diagramx': [319, -1, 188, -1], 'generators': [127651814341427291341507040516023521515254, 271353676394454377792702129150099764, 127584479652529225029754187324304, 26978572725239511210388, 5839768424695184672943013074, 17684330570401657831907612774644, 418802671169936714973312003, 3259463770706534265128308294164584130, 10628907036246685625578073782240332522387, 295241022183162551778698202493878165145, 244049793984571441653890772022859036635918, 4865804190709907763], 'label': '944784.rx.4.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.D', 'old_label': '4.i1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.I', 'subgroup_fusion': None, 'weyl_group': '472392.sf'}
    • id: 259934780
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 6, 'diagramx': [3198, -1, 2480, -1], 'generators': [127653180850277563395451136404310139427799, 3259463770706482556228691568819768918, 271353676394454377792702129150099764, 5451961195039184958188511090, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 295241022183162500077218895303207320365, 418802671169936714973312003, 275959908447240901527518204918667984917730], 'label': '944784.rx.36.BI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '36.bi1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BI', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934781
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BJ', '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': '11664.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1366, -1, 1935, -1], 'generators': [3259463770706482556228691568819768918, 271353676394454377792702129150099764, 5451961195039184958188511090, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 295241022183162500077218895303207320365, 4897592487934059020552616504200037091, 418802671169936714973312003, 127584479652529225029754187324304], 'label': '944784.rx.36.BJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.N', 'old_label': '36.bj1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BJ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934782
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [66, -1, 1548, -1], 'generators': [127653180850277563395451136404310139427799, 3259463770706482556228691568819768918, 271353676394454377792702129150099764, 74455662644931141873120408090549992132999, 5451961195039184958188511090, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 418802671169936714973312003, 275959908447240901527518204918667984917730], 'label': '944784.rx.36.BK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '36.bk1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BK', 'subgroup_fusion': None, 'weyl_group': '1944.2346'}
    • id: 259934783
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BL', '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': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [21, -1, 1535, -1], 'generators': [202098242143948411094716526875379787657842, 275959908356282400148388405536365721106068, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 275964517152191334761235988215884490240145, 275959908356289079275440747840674972603584, 418802671169936714973312003, 127645855444463450935263691676363382286080], 'label': '944784.rx.36.BL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.D', 'old_label': '36.bl1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BL', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934784
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BM', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [1794, -1, 2062, -1], 'generators': [202098242143948411094716526875379787657842, 5839768424695184672943013074, 1637963889910918891380036126878157955, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 3259463770706534265128308294164584130, 418802671169936714973312003], 'label': '944784.rx.36.BM', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '36.bm1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BM', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934785
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BN', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 6, 'diagramx': [2144, -1, 2166, -1], 'generators': [202098242143948411094716526875379787657842, 1637963889910918891380036126878157955, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 127651814341429807909604074251360238547908, 4865804190709907763, 418802671169936714973312003, 127645855444463450935263691676363382286080], 'label': '944784.rx.36.BN', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '36.bn1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BN', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934786
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BO', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 12, 'diagramx': [2760, -1, 2350, -1], 'generators': [17684330570401657831907612774644, 191472051032343538037001321677135365749125, 4865804190709907763, 271353676394454377792702129150099764, 418802671169936714973312003, 127647476807622762102329289457037538864451, 3259463770706534265128308294164584130, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BO', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '36.bo1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BO', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934787
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BP', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 36, 'diagramx': [646, -1, 1721, -1], 'generators': [17684330570401657831907612774644, 191472051032343538037001321677135365749125, 4865804190709907763, 271353676394454377792702129150099764, 244049793984571441653890772022859036635918, 275962352962651695408739719452801998844164, 418802671169936714973312003, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BP', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.N', 'old_label': '36.bp1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BP', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934788
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BQ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 36, 'diagramx': [693, -1, 1735, -1], 'generators': [244049793984571441653890772022859036635918, 74160421623357756629837947595896246623624, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 418802671169936714973312003, 237475337926402312641649968687507, 275962352962651695408739719452801998844164], 'label': '944784.rx.36.BQ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.N', 'old_label': '36.bq1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BQ', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934789
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BR', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 18, 'diagramx': [464, -1, 1666, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 212138601873112849117857797372094988957171, 7045161123238576809862975502817589074, 418802671169936714973312003, 244345035006754604316143447273355769799735, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BR', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '36.br1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BR', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934790
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '6.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '6.A', 'coset_action_label': None, 'count': 2, 'diagramx': [343, 1482, 308, 4172], 'generators': [17684330570401657831907612774644, 191472051032343538037001321677135365749125, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 351029896963370416307039779027355634051868, 418802671169936714973312003, 237475337926402312641649968687507, 3259463770706534265128308294164584130, 2164427020010358586814490815719916131, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.6.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '944784.rx', '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: 259934791
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BS', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '72.A', 'coset_action_label': None, 'count': 6, 'diagramx': [140, -1, 1570, -1], 'generators': [17684330570401657831907612774644, 191472051032343538037001321677135365749125, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 3259463770706534265128308294164584130, 26978572725239511210388, 351323236716841457582981799391071604180532, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BS', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '36.bs1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BS', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934792
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BT', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.B', 'coset_action_label': None, 'count': 18, 'diagramx': [517, -1, 1682, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 244049793984571441653890772022859036635918, 127651814341427291341507040516023521515254, 418802671169936714973312003, 201803017568052333615023641991654524717707, 3259463770706534265128308294164584130, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BT', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.M', 'old_label': '36.bt1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BT', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934793
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BU', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.B', 'coset_action_label': None, 'count': 6, 'diagramx': [172, -1, 1579, -1], 'generators': [17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 7045161123238576809862975502817589074, 418802671169936714973312003, 106366040138324400171129494222053604186877, 275959908429557765295566733700529155577014, 26978572725239511210388, 74160421623357756629837947595896246623624, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BU', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '36.bu1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BU', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934794
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BV', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [740, -1, 1749, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127645855243625415731227241613297048104133, 418802671169936714973312003, 223379983725808667004030579950474630737224, 5839768424695184672943013074, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BV', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BV', 'old_label': '36.bv1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BV', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934795
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BW', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 72, 'diagramx': [1663, -1, 2023, -1], 'generators': [17684330570401657831907612774644, 275956920273672869823695745448108005346708, 4865804190709907763, 295241022183162551778698202493878165145, 271353676394454377792702129150099764, 418802671169936714973312003, 106366040138324400171129494222053604186877, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BW', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BW', 'old_label': '36.bw1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BW', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934796
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BX', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 72, 'diagramx': [1618, -1, 2010, -1], 'generators': [275959908282403518690324474174807783429810, 371691303737740025833144366518736235139243, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 295241022183162551778698202493878165145, 10628907036246685625578073782240332522387, 4865804190709907763, 418802671169936714973312003, 275962352962651695408739719452801998844164], 'label': '944784.rx.36.BX', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BX', 'old_label': '36.bx1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BX', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934797
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BY', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '1296.A', 'coset_action_label': None, 'count': 36, 'diagramx': [285, -1, 1613, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127645855243625415731227241613297048104133, 418802671169936714973312003, 106366040138324400171129494222053604186877, 127651814341429807909604074251360238547908, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.BY', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.BY', 'old_label': '36.by1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BY', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934798
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.BZ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 36, 'diagramx': [920, -1, 1802, -1], 'generators': [244049793984571441653890772022859036635918, 26978572725239511210388, 271353676394454377792702129150099764, 17684330570401657831907612774644, 295241022183162551778698202493878165145, 10628907036246685625578073782240332522387, 4865804190709907763, 418802671169936714973312003, 237475337926402312641649968687507, 275962352962651695408739719452801998844164], 'label': '944784.rx.36.BZ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.N', 'old_label': '36.bz1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.BZ', 'subgroup_fusion': None, 'weyl_group': '52488.nf'}
    • id: 259934799
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CA', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1752, -1, 2050, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 7045161123238576809862975502817589074, 418802671169936714973312003, 275959908429557765295566733700529155577014, 351031526695267069720947200233457138933610, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.CA', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.L', 'old_label': '36.ca1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CA', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934800
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CB', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.B', 'coset_action_label': None, 'count': 18, 'diagramx': [1707, -1, 2037, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 116401765560895338504280564304072207705037, 3259463770706534265128308294164584130, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.CB', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.M', 'old_label': '36.cb1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CB', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934801
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '6.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.B', 'coset_action_label': None, 'count': 6, 'diagramx': [382, -1, 320, -1], 'generators': [127645855444463450935263691676363382286080, 17684330570401657831907612774644, 275958286791666469200145785571593592407092, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 74455662644931141873120408090549992132999, 418802671169936714973312003, 127651814341429807909604074251360238547908, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.6.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.B', 'old_label': '6.b1', 'projective_image': '944784.rx', '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: 259934802
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CC', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 36, 'diagramx': [245, -1, 1601, -1], 'generators': [17684330570401657831907612774644, 7045353424012272794609943097809550320, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 106366040138324400171129494222053604186877, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.CC', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.N', 'old_label': '36.cc1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CC', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934803
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CD', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1185, -1, 1881, -1], 'generators': [17684330570401657831907612774644, 191472051032343538037001321677135365749125, 4865804190709907763, 271353676394454377792702129150099764, 275962352962651695408739719452801998844164, 418802671169936714973312003, 233719098921583711142790561702055522185026, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.CD', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '36.cd1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CD', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934804
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CE', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '432.A', 'coset_action_label': None, 'count': 12, 'diagramx': [1217, -1, 1891, -1], 'generators': [17684330570401657831907612774644, 7045353424012272794609943097809550320, 4865804190709907763, 271353676394454377792702129150099764, 127651814341427291341507040516023521515254, 418802671169936714973312003, 106366040138324400171129494222053604186877, 201803017568052333615023641991654524717707, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.CE', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.I', 'old_label': '36.ce1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CE', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934805
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CF', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1405, -1, 1947, -1], 'generators': [3259463770706482556228691568819768918, 271353676394454377792702129150099764, 74455662644931141873120408090549992132999, 5451961195039184958188511090, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 295241022183162500077218895303207320365, 418802671169936714973312003, 275959908447240901527518204918667984917730], 'label': '944784.rx.36.CF', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '36.cf1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CF', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934806
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CG', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '72.B', 'coset_action_label': None, 'count': 9, 'diagramx': [603, -1, 1708, -1], 'generators': [17684330570401657831907612774644, 295241022183162551778698202493878165145, 4865804190709907763, 271353676394454377792702129150099764, 74455662644931141873120408090549992132999, 7045161123238576809862975502817589074, 418802671169936714973312003, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.CG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '36.cg1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CG', 'subgroup_fusion': None, 'weyl_group': '104976.nt'}
    • id: 259934807
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CH', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1576, -1, 1997, -1], 'generators': [3259463770706482556228691568819768918, 276253511368172292103428529232088284191290, 271353676394454377792702129150099764, 5451961195039184958188511090, 17684330570401657831907612774644, 10628907036246685625578073782240332522387, 4865804190709907763, 275959908438703609024017568292107531726773, 418802671169936714973312003, 339786375342376859406862345477654444615106], 'label': '944784.rx.36.CH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.C', 'old_label': '36.ch1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CH', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934808
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CI', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 36, 'diagramx': [1075, -1, 1848, -1], 'generators': [300393531205830864744611142798001520394, 202098242143948411094716526875379787657842, 5839768424695184672943013074, 271353676394454377792702129150099764, 17684330570401657831907612774644, 275959908429557765295566733700529155577014, 10628907036246685625578073782240332522387, 4865804190709907763, 418802671169936714973312003, 7045161119044966062548011258795331157], 'label': '944784.rx.36.CI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.CI', 'old_label': '36.ci1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CI', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934809
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CJ', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 9, 'diagramx': [106, -1, 1560, -1], 'generators': [276253511368172292103428529232088284191290, 17684330570401657831907612774644, 4865804190709907763, 271353676394454377792702129150099764, 339786375342376859406862345477654444615106, 7045161123238576809862975502817589074, 418802671169936714973312003, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.CJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.D', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '36.cj1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CJ', 'subgroup_fusion': None, 'weyl_group': '104976.nt'}
    • id: 259934810
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CK', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': None, 'contains': None, 'core': '144.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1488, -1, 1971, -1], 'generators': [17684330570401657831907612774644, 244346104944920001937955052654412440330385, 4865804190709907763, 271353676394454377792702129150099764, 191475565385802865750922838136124265049105, 418802671169936714973312003, 7045161123238576809862975502817589074, 275959908429557765295566733700529155577014, 26978572725239511210388, 10628907036246685625578073782240332522387], 'label': '944784.rx.36.CK', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.E', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.A', 'old_label': '36.ck1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CK', 'subgroup_fusion': None, 'weyl_group': None}
    • id: 259934811
      {'ambient': '944784.rx', 'aut_centralizer_order': None, 'aut_label': '36.CL', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '11664.A', 'coset_action_label': None, 'count': 18, 'diagramx': [1445, -1, 1958, -1], 'generators': [202098242143948411094716526875379787657842, 3259463770706482556228691568819768918, 127651814341427291341507040516023521515254, 271353676394454377792702129150099764, 17684330570401657831907612774644, 298500485344092212256993321837624199679, 10628907036246685625578073782240332522387, 4865804190709907763, 3259463762317318627384352499074778384, 418802671169936714973312003], 'label': '944784.rx.36.CL', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.C', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.D', 'old_label': '36.cl1', 'projective_image': '944784.rx', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.CL', 'subgroup_fusion': None, 'weyl_group': None}